This is an EFA for the ratings of the self on all items. Only 70 of the 77 have totally complete data, and to be conservative, I’m just looking at those 70. We don’t lose too much without those 7 and it’s easier to satisfy assumptions of EFA without missing data. Haven’t looked closely at what they’re missing yet though.
These histograms by themselves tell a really interesting story – you can see that there is a some overlap between Acc and Cont ratings, but some items distinguish between them. These line up with a lot of our a priori ideas – see anger and jealousy. Pretty cool.
Aside from the status items, you also can see the scores on depression and substance use, among other things. Keep in mind the middle 2 CES_D items are reverse coded. SES ladder is mostly between 3-7 on a 9 point scale.
| desc | skew | pval | mean | sd |
|---|---|---|---|---|
| insecure_Self | -0.0283501 | 0.9019713 | 3.490000 | 1.7551943 |
| daring_Self | -0.0369397 | 0.8725091 | 3.250000 | 1.4728177 |
| stubborn_Self | -0.0579809 | 0.8012135 | 3.490000 | 1.5858911 |
| leader_Self | 0.1027514 | 0.6559274 | 3.310000 | 1.5419717 |
| outgoing_Self | -0.1224289 | 0.5958376 | 3.550000 | 1.7602514 |
| popular_Self | 0.1436750 | 0.5359458 | 3.292929 | 1.5859879 |
| trendy_Self | -0.1445669 | 0.5334386 | 3.454546 | 1.5536181 |
| athletic_Self | -0.1573981 | 0.4961474 | 3.540000 | 1.6231905 |
| plain_Self | 0.1663235 | 0.4742817 | 3.232323 | 1.5896880 |
| pushover_Self | 0.1733206 | 0.4561013 | 3.010101 | 1.6567423 |
| confident_Self | -0.1805505 | 0.4377608 | 3.686869 | 1.5626147 |
| flirty_Self | 0.1910091 | 0.4120430 | 3.121212 | 1.6242595 |
| lonely_Self | 0.2134421 | 0.3580291 | 3.170000 | 1.6517820 |
| jealous_Self | 0.2166837 | 0.3509063 | 2.900000 | 1.4389952 |
| admired_Self | -0.2248039 | 0.3334858 | 3.610000 | 1.4832056 |
| loner_Self | 0.2408992 | 0.3007352 | 3.120000 | 1.7249213 |
| awkward_Self | -0.2509980 | 0.2813861 | 3.600000 | 1.6817499 |
| poor_Self | 0.2688930 | 0.2493376 | 2.840000 | 1.5486716 |
| dependent_Self | -0.3042124 | 0.1941856 | 3.650000 | 1.4310764 |
| risky_Self | 0.3162972 | 0.1776644 | 2.900000 | 1.4459976 |
| shy_Self | -0.3172830 | 0.1763672 | 3.850000 | 1.7196135 |
| cool_Self | -0.3321158 | 0.1595970 | 3.767677 | 1.4971284 |
| depressed_Self | 0.3563828 | 0.1324318 | 2.989899 | 1.6751177 |
| social_Self | -0.3708593 | 0.1164910 | 3.910000 | 1.6023657 |
| selfish_Self | 0.4277253 | 0.0737972 | 2.646465 | 1.4308063 |
| boring _Self | 0.4287829 | 0.0718664 | 2.770000 | 1.5166084 |
| patient_Self | -0.4599712 | 0.0557251 | 4.141414 | 1.3477881 |
| studious_Self | -0.4838010 | 0.0440607 | 4.370000 | 1.2764772 |
| adventurous_Self | -0.4871470 | 0.0427308 | 3.960000 | 1.4696938 |
| genuine_Self | -0.5502226 | 0.0235596 | 4.730000 | 1.0996326 |
| considerate_Self | -0.5567995 | 0.0221008 | 4.810000 | 1.0317681 |
| bossy_Self | 0.5578755 | 0.0218702 | 2.610000 | 1.5034976 |
| lazy_Self | 0.5746806 | 0.0190660 | 2.636364 | 1.5349968 |
| grumpy_Self | 0.5781332 | 0.0184309 | 2.646465 | 1.5139699 |
| caring_Self | -0.6049512 | 0.0137084 | 4.740000 | 1.0882290 |
| attractive_Self | -0.6192752 | 0.0118559 | 4.090000 | 1.3640033 |
| comforting_Self | -0.6278347 | 0.0108637 | 4.160000 | 1.3905889 |
| funny_Self | -0.6287765 | 0.0107594 | 4.210000 | 1.2815316 |
| rule-follower_Self | -0.6307734 | 0.0105414 | 4.300000 | 1.3521401 |
| controlling_Self | 0.6337901 | 0.0102200 | 2.600000 | 1.4839206 |
| calm_Self | -0.6507185 | 0.0088741 | 4.444444 | 1.1712737 |
| humble_Self | -0.6776478 | 0.0064745 | 4.360000 | 1.2351747 |
| helpful_Self | -0.6789290 | 0.0063877 | 4.780000 | 1.0596359 |
| agressive_Self | 0.7324172 | 0.0037556 | 2.333333 | 1.4356965 |
| giving_Self | -0.7483863 | 0.0030331 | 4.560000 | 1.2578642 |
| snobby_Self | 0.7502175 | 0.0031001 | 2.323232 | 1.4765395 |
| angry_Self | 0.7731570 | 0.0023127 | 2.480000 | 1.4666667 |
| honest_Self | -0.7748193 | 0.0023727 | 4.595960 | 1.2030505 |
| motivated_Self | -0.7847003 | 0.0021295 | 4.444444 | 1.2874767 |
| rude_Self | 0.8024367 | 0.0016730 | 2.170000 | 1.2953296 |
| mean_Self | 0.8178574 | 0.0014088 | 2.230000 | 1.4131775 |
| nice_Self | -0.8676875 | 0.0008039 | 4.880000 | 0.9773185 |
| welcoming_Self | -0.8746451 | 0.0007429 | 4.550000 | 1.2007994 |
| friendly_Self | -0.8770667 | 0.0007227 | 4.650000 | 1.2583057 |
| ugly_Self | 0.9027683 | 0.0005391 | 2.390000 | 1.4347421 |
| sympathetic_Self | -0.9293323 | 0.0004210 | 4.525252 | 1.3041804 |
| trustworthy_Self | -1.0070150 | 0.0001616 | 4.830000 | 1.0546195 |
| smart_Self | -1.0217586 | 0.0001552 | 4.918367 | 0.9809891 |
| fair_Self | -1.0710441 | 0.0000764 | 4.630000 | 1.2605514 |
| fake_Self | 1.0872091 | 0.0000632 | 1.930000 | 1.1997895 |
| loyal_Self | -1.1144612 | 0.0000458 | 4.770000 | 1.1964172 |
| respectful_Self | -1.2988493 | 0.0000052 | 4.870000 | 1.0885539 |
The plot below seems to indicate that a good number of people consider themselves high status in both ways (all responses in the top right quadrant). There doesn’t seem to be perfect separation between the two. However, note that the bottom left quadrant reflects responses from people that think neither type of status describes them well (31 people). Also note that the overlap group is only comprises 13 people. Number of primarily accepted status = 39, and primarily controversial status participants = 15.
| Cont_v_Acc | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 11 | 6 | 5 | 7 | 7 | 6 |
| 2 | 2 | 1 | 2 | 6 | 3 | 3 |
| 3 | 1 | 1 | 2 | 3 | 4 | 0 |
| 4 | 1 | 1 | 5 | 1 | 5 | 0 |
| 5 | 1 | 1 | 2 | 3 | 3 | 0 |
| 6 | 3 | 0 | 1 | 0 | 0 | 1 |
We want to keep all the prosocial items we can, so let’s see what correlates with it and just remove those items from the factor analysis. Then we can see what else sticks together, and use that as the second one.
## risky_Self shy_Self daring_Self
## -0.03381114 -0.05986764 0.06750512
## stubborn_Self flirty_Self dependent_Self
## -0.07525814 0.09126158 -0.09259563
## trendy_Self plain_Self controlling_Self
## 0.13226106 -0.13549504 -0.13905925
## outgoing_Self cool_Self lonely_Self
## 0.15062385 0.15787746 -0.16395309
## rule-follower_Self awkward_Self athletic_Self
## 0.16834631 -0.16862502 0.18087389
## leader_Self insecure_Self bossy_Self
## 0.19548830 -0.19982895 -0.21179868
## adventurous_Self pushover_Self loner_Self
## 0.21866287 -0.21886119 -0.22048685
## social_Self popular_Self depressed_Self
## 0.22651835 0.22707536 -0.23225008
## admired_Self poor_Self confident_Self
## 0.23982741 -0.25653584 0.26793293
## jealous_Self ugly_Self agressive_Self
## -0.27351833 -0.27552265 -0.28895723
## boring _Self funny_Self comforting_Self
## -0.29080782 0.29730289 0.29954552
## attractive_Self selfish_Self rude_Self
## 0.30163030 -0.30956400 -0.30957320
## respectful_Self angry_Self calm_Self
## 0.31089893 -0.31100697 0.31631639
## patient_Self loyal_Self humble_Self
## 0.31727518 0.32366047 0.32510420
## grumpy_Self motivated_Self studious_Self
## -0.32839170 0.32983626 0.33414129
## snobby_Self fake_Self giving_Self
## -0.34542901 -0.35220158 0.37118279
## mean_Self fair_Self sympathetic_Self
## -0.37379551 0.39606736 0.39625965
## genuine_Self welcoming_Self friendly_Self
## 0.41450943 0.41602265 0.41877785
## considerate_Self caring_Self nice_Self
## 0.43528960 0.44409166 0.47053254
## trustworthy_Self
## 0.48584338
First thing, let’s see what items are best at predicting status using regularized regression for multinomial responses. This uses cross validation to give us the set of predictors that leads to the best out-of-sample prediction (least error).
The first plot shows how prediction error varies as a function of the number of parameters in the model, and how much weight each gets (the size of the coefficient).
The second set of plots actually show the size of each coefficient predicting both types of status as the constraint parameter, lambda, is tightened (left-to-right).
This table shows all the non-zero coefficients
| xName | ContStat | AccStat |
|---|---|---|
| (Intercept) | 1.424 | 2.787 |
| admired_Self | 0.079 | 0.074 |
| agressive_Self | 0.065 | 0.049 |
| angry_Self | 0.140 | -0.105 |
| awkward_Self | 0.016 | -0.023 |
| cool_Self | 0.047 | 0.052 |
| grumpy_Self | 0.043 | -0.043 |
| jealous_Self | 0.086 | -0.016 |
| leader_Self | -0.012 | 0.102 |
| mean_Self | 0.035 | 0.005 |
| poor_Self | 0.019 | -0.113 |
| popular_Self | 0.020 | 0.107 |
| risky_Self | 0.047 | -0.044 |
| rude_Self | 0.128 | -0.019 |
| rulefollower_Self | -0.054 | 0.061 |
| selfish_Self | 0.003 | -0.001 |
| shy_Self | 0.033 | -0.094 |
| snobby_Self | 0.014 | 0.008 |
| social_Self | 0.040 | 0.177 |
| studious_Self | -0.029 | 0.002 |
| trendy_Self | 0.055 | 0.130 |
If we were merely trying to predict status from a future data set containing these same items, the above table would be the best subset to use. I’ll come back to these later, because I think they’ll be useful in our final item selection.
While we’re interested in predicting status, we’re not actually asking about status. Rather, we’re asking about traits that we think relate to status. So while the above set of items might tell us who is likely to have one or the other kind of status, in the context of an fMRI analysis it would be hard to argue that activity observed during self evaluation of these traits is some measure of status-related brain activity.
The more traditional approach would be to use EFA. What we hope to get is 2 factors the correspond to Accepted High Status and Controversial High Status.
However, the scree plot shows very clearly a 4 factor solution will account for most of the variance, with no real gain if we increase beyond 4.
## Factor Analysis using method = pa
## Call: fa(r = select(selfRateDat, -matches("SelfPop")), nfactors = 3,
## rotate = "oblimin", scores = "tenBerge", fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PA3 PA1 PA2 h2 u2 com
## insecure_Self 31 -0.86 0.09 0.20 0.72 0.28 1.1
## lonely_Self 35 -0.84 0.14 0.28 0.69 0.31 1.3
## depressed_Self 19 -0.82 0.10 0.29 0.69 0.31 1.3
## loner_Self 36 -0.79 -0.03 0.09 0.64 0.36 1.0
## awkward_Self 7 -0.78 0.16 0.26 0.59 0.41 1.3
## confident_Self 13 0.77 0.20 0.15 0.74 0.26 1.2
## trendy_Self 59 0.76 0.05 0.25 0.67 0.33 1.2
## shy_Self 52 -0.73 0.22 -0.02 0.49 0.51 1.2
## popular_Self 45 0.72 0.23 0.27 0.73 0.27 1.5
## social_Self 55 0.71 0.22 0.27 0.71 0.29 1.5
## plain_Self 43 -0.67 0.10 0.09 0.42 0.58 1.1
## flirty_Self 22 0.64 0.04 0.27 0.51 0.49 1.4
## boring _Self 8 -0.64 -0.03 0.23 0.46 0.54 1.3
## admired_Self 1 0.62 0.25 0.36 0.65 0.35 2.0
## outgoing_Self 41 0.62 0.14 0.24 0.52 0.48 1.4
## attractive_Self 6 0.61 0.33 0.22 0.63 0.37 1.8
## cool_Self 16 0.60 0.27 0.41 0.68 0.32 2.2
## ugly_Self 61 -0.59 -0.18 0.17 0.47 0.53 1.4
## leader_Self 34 0.57 0.12 0.32 0.49 0.51 1.7
## pushover_Self 46 -0.57 0.05 0.22 0.35 0.65 1.3
## adventurous_Self 2 0.50 0.29 0.33 0.51 0.49 2.4
## funny_Self 24 0.49 0.30 0.15 0.43 0.57 1.9
## poor_Self 44 -0.46 -0.22 0.33 0.45 0.55 2.3
## daring_Self 17 0.43 0.08 0.38 0.36 0.64 2.0
## athletic_Self 5 0.31 0.18 0.10 0.17 0.83 1.9
## nice_Self 40 -0.05 0.84 -0.10 0.73 0.27 1.0
## considerate_Self 14 -0.15 0.83 -0.10 0.69 0.31 1.1
## helpful_Self 28 0.08 0.79 0.03 0.66 0.34 1.0
## genuine_Self 25 -0.03 0.77 -0.02 0.58 0.42 1.0
## caring_Self 11 0.04 0.76 -0.02 0.59 0.41 1.0
## loyal_Self 37 -0.12 0.74 0.00 0.51 0.49 1.1
## friendly_Self 23 0.13 0.72 -0.02 0.59 0.41 1.1
## trustworthy_Self 60 0.11 0.72 -0.04 0.58 0.42 1.0
## giving_Self 26 0.04 0.71 0.03 0.52 0.48 1.0
## sympathetic_Self 58 0.00 0.71 -0.06 0.52 0.48 1.0
## welcoming_Self 62 0.11 0.68 -0.15 0.58 0.42 1.2
## fair_Self 20 0.05 0.59 -0.20 0.46 0.54 1.2
## respectful_Self 47 0.00 0.57 -0.06 0.35 0.65 1.0
## humble_Self 30 -0.25 0.56 -0.20 0.38 0.62 1.7
## calm_Self 10 0.15 0.55 -0.15 0.44 0.56 1.3
## honest_Self 29 0.20 0.50 -0.14 0.40 0.60 1.5
## rule-follower_Self 50 -0.20 0.47 -0.05 0.22 0.78 1.4
## studious_Self 57 -0.10 0.47 -0.05 0.22 0.78 1.1
## motivated_Self 39 0.16 0.46 -0.03 0.29 0.71 1.2
## smart_Self 53 0.03 0.45 -0.07 0.23 0.77 1.1
## comforting_Self 12 0.34 0.44 0.00 0.40 0.60 1.9
## patient_Self 42 0.13 0.43 -0.27 0.36 0.64 1.9
## controlling_Self 15 0.23 -0.01 0.74 0.61 0.39 1.2
## snobby_Self 54 0.02 -0.29 0.72 0.68 0.32 1.3
## bossy_Self 9 0.23 -0.14 0.72 0.62 0.38 1.3
## angry_Self 4 -0.32 -0.09 0.71 0.64 0.36 1.4
## rude_Self 49 0.04 -0.26 0.70 0.62 0.38 1.3
## mean_Self 38 0.01 -0.32 0.70 0.67 0.33 1.4
## grumpy_Self 27 -0.42 -0.05 0.66 0.62 0.38 1.7
## agressive_Self 3 0.13 -0.24 0.66 0.55 0.45 1.4
## selfish_Self 51 -0.10 -0.27 0.60 0.52 0.48 1.5
## jealous_Self 32 -0.39 0.02 0.56 0.44 0.56 1.8
## lazy_Self 33 -0.15 -0.16 0.49 0.33 0.67 1.4
## fake_Self 21 -0.14 -0.40 0.48 0.51 0.49 2.1
## stubborn_Self 56 -0.06 0.12 0.47 0.21 0.79 1.2
## risky_Self 48 0.22 -0.05 0.46 0.27 0.73 1.4
## dependent_Self 18 -0.28 0.18 0.39 0.19 0.81 2.3
##
## PA3 PA1 PA2
## SS loadings 12.44 11.27 7.84
## Proportion Var 0.20 0.18 0.13
## Cumulative Var 0.20 0.38 0.51
## Proportion Explained 0.39 0.36 0.25
## Cumulative Proportion 0.39 0.75 1.00
##
## With factor correlations of
## PA3 PA1 PA2
## PA3 1.00 0.31 0.04
## PA1 0.31 1.00 -0.19
## PA2 0.04 -0.19 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 1891 and the objective function was 72.05 with Chi Square of 5583.84
## The degrees of freedom for the model are 1708 and the objective function was 34.22
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.06
##
## The harmonic number of observations is 99 with the empirical chi square 1373.9 with prob < 1
## The total number of observations was 100 with MLE Chi Square = 2583.27 with prob < 6.4e-39
##
## Tucker Lewis Index of factoring reliability = 0.727
## RMSEA index = 0.1 and the 90 % confidence intervals are 0.066 0.077
## BIC = -5282.36
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy
## PA3 PA1 PA2
## Correlation of scores with factors 0.99 0.98 0.98
## Multiple R square of scores with factors 0.97 0.96 0.96
## Minimum correlation of possible factor scores 0.95 0.93 0.91
## Factor Analysis using method = pa
## Call: fa(r = select(selfRateDat, -matches("SelfPop")), nfactors = 2,
## rotate = "oblimin", scores = "tenBerge", fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PA1 PA2 h2 u2 com
## popular_Self 45 0.85 0.02 0.730 0.27 1.0
## social_Self 55 0.84 0.01 0.714 0.29 1.0
## confident_Self 13 0.84 0.09 0.740 0.26 1.0
## trendy_Self 59 0.83 -0.10 0.674 0.33 1.0
## cool_Self 16 0.81 -0.07 0.641 0.36 1.0
## admired_Self 1 0.80 -0.05 0.635 0.37 1.0
## attractive_Self 6 0.76 0.12 0.620 0.38 1.1
## outgoing_Self 41 0.73 -0.04 0.520 0.48 1.0
## flirty_Self 22 0.72 -0.14 0.511 0.49 1.1
## loner_Self 36 -0.71 -0.15 0.567 0.43 1.1
## leader_Self 34 0.70 -0.12 0.482 0.52 1.1
## insecure_Self 31 -0.69 -0.14 0.537 0.46 1.1
## adventurous_Self 2 0.69 0.01 0.472 0.53 1.0
## shy_Self 52 -0.63 0.13 0.383 0.62 1.1
## lonely_Self 35 -0.62 -0.17 0.452 0.55 1.1
## depressed_Self 19 -0.62 -0.21 0.467 0.53 1.2
## funny_Self 24 0.61 0.15 0.420 0.58 1.1
## daring_Self 17 0.58 -0.20 0.342 0.66 1.2
## awkward_Self 7 -0.57 -0.13 0.371 0.63 1.1
## plain_Self 43 -0.56 -0.04 0.329 0.67 1.0
## ugly_Self 61 -0.53 -0.31 0.439 0.56 1.6
## boring _Self 8 -0.51 -0.25 0.366 0.63 1.4
## comforting_Self 12 0.44 0.36 0.383 0.62 1.9
## pushover_Self 46 -0.43 -0.17 0.238 0.76 1.3
## athletic_Self 5 0.39 0.09 0.169 0.83 1.1
## mean_Self 38 0.20 -0.79 0.607 0.39 1.1
## snobby_Self 54 0.23 -0.78 0.608 0.39 1.2
## rude_Self 49 0.25 -0.74 0.547 0.45 1.2
## nice_Self 40 0.15 0.73 0.587 0.41 1.1
## considerate_Self 14 0.05 0.71 0.525 0.48 1.0
## fake_Self 21 -0.05 -0.70 0.500 0.50 1.0
## agressive_Self 3 0.31 -0.69 0.503 0.50 1.4
## selfish_Self 51 0.07 -0.69 0.461 0.54 1.0
## welcoming_Self 62 0.24 0.65 0.538 0.46 1.3
## bossy_Self 9 0.47 -0.65 0.535 0.47 1.8
## angry_Self 4 -0.03 -0.64 0.416 0.58 1.0
## fair_Self 20 0.14 0.62 0.433 0.57 1.1
## genuine_Self 25 0.18 0.61 0.441 0.56 1.2
## caring_Self 11 0.24 0.60 0.470 0.53 1.3
## helpful_Self 28 0.31 0.60 0.512 0.49 1.5
## sympathetic_Self 58 0.18 0.59 0.420 0.58 1.2
## trustworthy_Self 60 0.29 0.59 0.492 0.51 1.5
## friendly_Self 23 0.32 0.58 0.498 0.50 1.5
## humble_Self 30 -0.16 0.58 0.327 0.67 1.2
## grumpy_Self 27 -0.14 -0.57 0.376 0.62 1.1
## loyal_Self 37 0.10 0.57 0.350 0.65 1.1
## calm_Self 10 0.24 0.56 0.421 0.58 1.3
## patient_Self 42 0.14 0.56 0.361 0.64 1.1
## controlling_Self 15 0.51 -0.56 0.475 0.53 2.0
## giving_Self 26 0.25 0.53 0.389 0.61 1.4
## lazy_Self 33 0.01 -0.52 0.266 0.73 1.0
## honest_Self 29 0.28 0.51 0.387 0.61 1.5
## respectful_Self 47 0.14 0.49 0.288 0.71 1.2
## poor_Self 44 -0.36 -0.46 0.405 0.60 1.9
## jealous_Self 32 -0.14 -0.44 0.236 0.76 1.2
## smart_Self 53 0.13 0.41 0.202 0.80 1.2
## studious_Self 57 0.02 0.40 0.162 0.84 1.0
## motivated_Self 39 0.27 0.39 0.263 0.74 1.8
## rule-follower_Self 50 -0.08 0.39 0.150 0.85 1.1
## risky_Self 48 0.38 -0.38 0.242 0.76 2.0
## stubborn_Self 56 0.17 -0.28 0.088 0.91 1.6
## dependent_Self 18 -0.05 -0.18 0.039 0.96 1.2
##
## PA1 PA2
## SS loadings 13.53 13.19
## Proportion Var 0.22 0.21
## Cumulative Var 0.22 0.43
## Proportion Explained 0.51 0.49
## Cumulative Proportion 0.51 1.00
##
## With factor correlations of
## PA1 PA2
## PA1 1.00 0.17
## PA2 0.17 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 1891 and the objective function was 72.05 with Chi Square of 5583.84
## The degrees of freedom for the model are 1768 and the objective function was 41.33
##
## The root mean square of the residuals (RMSR) is 0.1
## The df corrected root mean square of the residuals is 0.1
##
## The harmonic number of observations is 99 with the empirical chi square 3502.54 with prob < 8.8e-117
## The total number of observations was 100 with MLE Chi Square = 3147.64 with prob < 1.2e-80
##
## Tucker Lewis Index of factoring reliability = 0.59
## RMSEA index = 0.115 and the 90 % confidence intervals are 0.083 0.093
## BIC = -4994.3
## Fit based upon off diagonal values = 0.91
## Measures of factor score adequacy
## PA1 PA2
## Correlation of scores with factors 0.99 0.98
## Multiple R square of scores with factors 0.97 0.96
## Minimum correlation of possible factor scores 0.95 0.93
Here’s the raw output, if you like, but see below for a prettier table. Notice the factors are allowed to correlate.
## Factor Analysis using method = pa
## Call: fa(r = select(selfRateDat, -matches("SelfPop")), nfactors = 4,
## rotate = "oblimin", scores = "tenBerge", fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PA3 PA1 PA2 PA4 h2 u2 com
## depressed_Self 19 0.91 0.11 0.16 0.16 0.76 0.24 1.2
## insecure_Self 31 0.89 0.09 0.10 0.05 0.75 0.25 1.1
## lonely_Self 35 0.83 0.13 0.23 -0.05 0.69 0.31 1.2
## awkward_Self 7 0.83 0.16 0.16 0.08 0.62 0.38 1.2
## trendy_Self 59 -0.76 0.06 0.33 -0.01 0.72 0.28 1.4
## confident_Self 13 -0.76 0.21 0.21 0.01 0.76 0.24 1.3
## loner_Self 36 0.74 -0.05 0.08 -0.12 0.64 0.36 1.1
## popular_Self 45 -0.69 0.24 0.30 0.06 0.74 0.26 1.7
## plain_Self 43 0.66 0.09 0.06 -0.05 0.42 0.58 1.1
## shy_Self 52 0.62 0.19 0.05 -0.28 0.51 0.49 1.6
## social_Self 55 -0.60 0.25 0.21 0.27 0.72 0.28 2.1
## boring _Self 8 0.57 -0.05 0.27 -0.19 0.48 0.52 1.7
## outgoing_Self 41 -0.56 0.17 0.23 0.14 0.52 0.48 1.7
## flirty_Self 22 -0.55 0.06 0.24 0.21 0.51 0.49 1.7
## admired_Self 1 -0.55 0.27 0.34 0.17 0.65 0.35 2.4
## cool_Self 16 -0.54 0.29 0.41 0.12 0.68 0.32 2.6
## leader_Self 34 -0.54 0.13 0.34 0.07 0.49 0.51 1.9
## ugly_Self 61 0.53 -0.20 0.19 -0.14 0.48 0.52 1.7
## pushover_Self 46 0.52 0.04 0.24 -0.14 0.35 0.65 1.6
## poor_Self 44 0.50 -0.22 0.26 0.08 0.46 0.54 2.0
## attractive_Self 6 -0.50 0.36 0.15 0.26 0.64 0.36 2.6
## funny_Self 24 -0.37 0.33 0.06 0.28 0.45 0.55 2.9
## athletic_Self 5 -0.28 0.20 0.10 0.07 0.17 0.83 2.2
## nice_Self 40 0.09 0.85 -0.16 0.06 0.74 0.26 1.1
## considerate_Self 14 0.18 0.84 -0.15 0.03 0.70 0.30 1.2
## helpful_Self 28 0.00 0.81 -0.06 0.15 0.69 0.31 1.1
## caring_Self 11 0.04 0.77 -0.10 0.14 0.62 0.38 1.1
## genuine_Self 25 -0.01 0.76 0.02 -0.14 0.59 0.41 1.1
## loyal_Self 37 0.09 0.73 0.02 -0.11 0.51 0.49 1.1
## trustworthy_Self 60 -0.05 0.73 -0.09 0.10 0.60 0.40 1.1
## friendly_Self 23 -0.11 0.72 -0.03 0.01 0.59 0.41 1.0
## giving_Self 26 -0.03 0.71 0.02 0.00 0.52 0.48 1.0
## sympathetic_Self 58 0.00 0.71 -0.05 -0.04 0.52 0.48 1.0
## welcoming_Self 62 -0.08 0.69 -0.18 0.05 0.59 0.41 1.2
## fair_Self 20 -0.08 0.59 -0.18 -0.08 0.46 0.54 1.3
## humble_Self 30 0.21 0.55 -0.18 -0.13 0.38 0.62 1.7
## respectful_Self 47 -0.17 0.55 0.13 -0.44 0.51 0.49 2.3
## calm_Self 10 -0.22 0.54 -0.07 -0.19 0.46 0.54 1.6
## honest_Self 29 -0.24 0.49 -0.09 -0.11 0.40 0.60 1.6
## smart_Self 53 0.01 0.46 -0.12 0.09 0.24 0.76 1.2
## motivated_Self 39 -0.25 0.44 0.09 -0.25 0.35 0.65 2.3
## studious_Self 57 -0.03 0.44 0.09 -0.34 0.30 0.70 2.0
## comforting_Self 12 -0.34 0.44 0.03 -0.01 0.40 0.60 1.9
## patient_Self 42 -0.18 0.42 -0.22 -0.12 0.36 0.64 2.1
## mean_Self 38 -0.02 -0.32 0.75 -0.04 0.72 0.28 1.4
## controlling_Self 15 -0.19 0.01 0.74 0.07 0.63 0.37 1.2
## snobby_Self 54 0.01 -0.28 0.73 0.05 0.70 0.30 1.3
## rude_Self 49 -0.03 -0.25 0.72 0.02 0.65 0.35 1.2
## bossy_Self 9 -0.17 -0.12 0.70 0.13 0.62 0.38 1.3
## angry_Self 4 0.38 -0.08 0.65 0.12 0.64 0.36 1.7
## grumpy_Self 27 0.46 -0.04 0.62 0.05 0.62 0.38 1.9
## agressive_Self 3 -0.05 -0.23 0.61 0.17 0.55 0.45 1.5
## selfish_Self 51 0.17 -0.26 0.54 0.17 0.52 0.48 1.9
## jealous_Self 32 0.42 0.02 0.52 0.04 0.44 0.56 1.9
## lazy_Self 33 0.17 -0.16 0.48 0.03 0.33 0.67 1.5
## fake_Self 21 0.16 -0.40 0.47 0.05 0.51 0.49 2.2
## dependent_Self 18 0.22 0.16 0.45 -0.17 0.23 0.77 2.1
## stubborn_Self 56 0.16 0.14 0.37 0.22 0.22 0.78 2.4
## daring_Self 17 -0.15 0.15 0.13 0.67 0.62 0.38 1.3
## risky_Self 48 0.05 0.02 0.22 0.63 0.50 0.50 1.2
## rule-follower_Self 50 -0.02 0.44 0.20 -0.59 0.49 0.51 2.1
## adventurous_Self 2 -0.31 0.34 0.17 0.45 0.60 0.40 3.0
##
## PA3 PA1 PA2 PA4
## SS loadings 11.60 11.35 7.23 3.18
## Proportion Var 0.19 0.18 0.12 0.05
## Cumulative Var 0.19 0.37 0.49 0.54
## Proportion Explained 0.35 0.34 0.22 0.10
## Cumulative Proportion 0.35 0.69 0.90 1.00
##
## With factor correlations of
## PA3 PA1 PA2 PA4
## PA3 1.00 -0.32 -0.01 -0.24
## PA1 -0.32 1.00 -0.17 -0.01
## PA2 -0.01 -0.17 1.00 0.27
## PA4 -0.24 -0.01 0.27 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 1891 and the objective function was 72.05 with Chi Square of 5583.84
## The degrees of freedom for the model are 1649 and the objective function was 32.32
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.06
##
## The harmonic number of observations is 99 with the empirical chi square 1098.85 with prob < 1
## The total number of observations was 100 with MLE Chi Square = 2418.93 with prob < 3e-32
##
## Tucker Lewis Index of factoring reliability = 0.748
## RMSEA index = 0.097 and the 90 % confidence intervals are 0.062 0.074
## BIC = -5175
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy
## PA3 PA1 PA2 PA4
## Correlation of scores with factors 0.99 0.98 0.98 0.93
## Multiple R square of scores with factors 0.98 0.97 0.96 0.87
## Minimum correlation of possible factor scores 0.96 0.93 0.91 0.73
We can look at how these factors group together too…
## Factor Analysis using method = pa
## Call: fa(r = selfRateFA$Phi, nfactors = 2, rotate = "oblimin", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2 com
## 1 0.61 -0.19 0.44 0.56 1.2
## 2 -0.58 -0.19 0.36 0.64 1.2
## 3 0.19 0.51 0.27 0.73 1.3
## 4 -0.14 0.59 0.38 0.62 1.1
##
## PA1 PA2
## SS loadings 0.77 0.68
## Proportion Var 0.19 0.17
## Cumulative Var 0.19 0.36
## Proportion Explained 0.53 0.47
## Cumulative Proportion 0.53 1.00
##
## With factor correlations of
## PA1 PA2
## PA1 1.0 -0.1
## PA2 -0.1 1.0
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 6 and the objective function was 0.28
## The degrees of freedom for the model are -1 and the objective function was 0
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is NA
##
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2
## Correlation of scores with factors 0.75 0.72
## Multiple R square of scores with factors 0.56 0.51
## Minimum correlation of possible factor scores 0.13 0.02
The four factors are pretty interpretable, if you ask me.
Here’s nice table:
| item | PA3 | PA1 | PA2 | PA4 | comm |
|---|---|---|---|---|---|
| depressed_Self | 0.91 | 0.11 | 0.16 | 0.16 | 0.758 |
| insecure_Self | 0.89 | 0.10 | 0.745 | ||
| lonely_Self | 0.83 | 0.13 | 0.23 | 0.692 | |
| awkward_Self | 0.83 | 0.16 | 0.16 | 0.620 | |
| trendy_Self | -0.76 | 0.33 | 0.715 | ||
| confident_Self | -0.76 | 0.21 | 0.21 | 0.762 | |
| loner_Self | 0.74 | -0.12 | 0.642 | ||
| popular_Self | -0.69 | 0.24 | 0.30 | 0.743 | |
| plain_Self | 0.66 | 0.424 | |||
| shy_Self | 0.62 | 0.19 | -0.28 | 0.506 | |
| social_Self | -0.60 | 0.25 | 0.21 | 0.27 | 0.720 |
| boring _Self | 0.57 | 0.27 | -0.19 | 0.479 | |
| outgoing_Self | -0.56 | 0.17 | 0.23 | 0.14 | 0.517 |
| flirty_Self | -0.55 | 0.24 | 0.21 | 0.508 | |
| admired_Self | -0.55 | 0.27 | 0.34 | 0.17 | 0.653 |
| cool_Self | -0.54 | 0.29 | 0.41 | 0.12 | 0.680 |
| leader_Self | -0.54 | 0.13 | 0.34 | 0.495 | |
| ugly_Self | 0.53 | -0.20 | 0.19 | -0.14 | 0.479 |
| pushover_Self | 0.52 | 0.24 | -0.14 | 0.352 | |
| poor_Self | 0.50 | -0.22 | 0.26 | 0.459 | |
| attractive_Self | -0.50 | 0.36 | 0.15 | 0.26 | 0.641 |
| funny_Self | -0.37 | 0.33 | 0.28 | 0.454 | |
| athletic_Self | -0.28 | 0.20 | 0.171 | ||
| nice_Self | 0.85 | -0.16 | 0.743 | ||
| considerate_Self | 0.18 | 0.84 | -0.15 | 0.699 | |
| helpful_Self | 0.81 | 0.15 | 0.689 | ||
| caring_Self | 0.77 | 0.14 | 0.625 | ||
| genuine_Self | 0.76 | -0.14 | 0.590 | ||
| loyal_Self | 0.73 | -0.11 | 0.514 | ||
| trustworthy_Self | 0.73 | 0.10 | 0.597 | ||
| friendly_Self | -0.11 | 0.72 | 0.591 | ||
| giving_Self | 0.71 | 0.516 | |||
| sympathetic_Self | 0.71 | 0.520 | |||
| welcoming_Self | 0.69 | -0.18 | 0.590 | ||
| fair_Self | 0.59 | -0.18 | 0.456 | ||
| humble_Self | 0.21 | 0.55 | -0.18 | -0.13 | 0.382 |
| respectful_Self | -0.17 | 0.55 | 0.13 | -0.44 | 0.508 |
| calm_Self | -0.22 | 0.54 | -0.19 | 0.460 | |
| honest_Self | -0.24 | 0.49 | -0.11 | 0.403 | |
| smart_Self | 0.46 | -0.12 | 0.243 | ||
| motivated_Self | -0.25 | 0.44 | -0.25 | 0.348 | |
| studious_Self | 0.44 | -0.34 | 0.296 | ||
| comforting_Self | -0.34 | 0.44 | 0.397 | ||
| patient_Self | -0.18 | 0.42 | -0.22 | -0.12 | 0.362 |
| mean_Self | -0.32 | 0.75 | 0.722 | ||
| controlling_Self | -0.19 | 0.74 | 0.631 | ||
| snobby_Self | -0.28 | 0.73 | 0.701 | ||
| rude_Self | -0.25 | 0.72 | 0.650 | ||
| bossy_Self | -0.17 | -0.12 | 0.70 | 0.13 | 0.623 |
| angry_Self | 0.38 | 0.65 | 0.12 | 0.640 | |
| grumpy_Self | 0.46 | 0.62 | 0.623 | ||
| agressive_Self | -0.23 | 0.61 | 0.17 | 0.553 | |
| selfish_Self | 0.17 | -0.26 | 0.54 | 0.17 | 0.522 |
| jealous_Self | 0.42 | 0.52 | 0.439 | ||
| lazy_Self | 0.17 | -0.16 | 0.48 | 0.331 | |
| fake_Self | 0.16 | -0.40 | 0.47 | 0.515 | |
| dependent_Self | 0.22 | 0.16 | 0.45 | -0.17 | 0.235 |
| stubborn_Self | 0.16 | 0.14 | 0.37 | 0.22 | 0.224 |
| daring_Self | -0.15 | 0.15 | 0.13 | 0.67 | 0.616 |
| risky_Self | 0.22 | 0.63 | 0.503 | ||
| rule-follower_Self | 0.44 | 0.20 | -0.59 | 0.492 | |
| adventurous_Self | -0.31 | 0.34 | 0.17 | 0.45 | 0.596 |
I think this plot is supposed to show how much separation we get.
We realized that we can drop the risk-taking items, and maybe drop some items that are the most skewed. Let’s do that and see what happens
## Factor Analysis using method = pa
## Call: fa(r = select(selfRateDat_lim, -matches("SelfPop")), nfactors = 2,
## rotate = "oblimin", scores = "tenBerge", fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PA1 PA2 h2 u2 com
## confident_Self 13 0.85 -0.06 0.741 0.26 1.0
## popular_Self 38 0.85 0.03 0.725 0.28 1.0
## social_Self 45 0.85 0.05 0.716 0.28 1.0
## trendy_Self 48 0.83 0.13 0.680 0.32 1.0
## cool_Self 16 0.80 0.13 0.641 0.36 1.1
## admired_Self 1 0.80 0.11 0.632 0.37 1.0
## attractive_Self 6 0.76 -0.05 0.593 0.41 1.0
## loner_Self 33 -0.74 0.14 0.586 0.41 1.1
## insecure_Self 28 -0.73 0.19 0.587 0.41 1.1
## outgoing_Self 34 0.72 0.08 0.518 0.48 1.0
## flirty_Self 20 0.71 0.18 0.514 0.49 1.1
## leader_Self 31 0.69 0.15 0.484 0.52 1.1
## adventurous_Self 2 0.69 0.08 0.473 0.53 1.0
## lonely_Self 32 -0.66 0.22 0.505 0.49 1.2
## depressed_Self 19 -0.66 0.28 0.541 0.46 1.4
## funny_Self 21 0.62 -0.09 0.407 0.59 1.0
## shy_Self 43 -0.62 -0.12 0.388 0.61 1.1
## awkward_Self 7 -0.60 0.22 0.428 0.57 1.3
## plain_Self 36 -0.57 0.08 0.338 0.66 1.0
## daring_Self 17 0.56 0.27 0.365 0.64 1.4
## boring _Self 8 -0.55 0.26 0.395 0.61 1.4
## comforting_Self 12 0.49 -0.31 0.361 0.64 1.7
## pushover_Self 39 -0.45 0.21 0.267 0.73 1.4
## athletic_Self 5 0.40 -0.07 0.172 0.83 1.1
## snobby_Self 44 0.12 0.79 0.627 0.37 1.0
## agressive_Self 3 0.22 0.73 0.551 0.45 1.2
## selfish_Self 42 -0.03 0.71 0.512 0.49 1.0
## bossy_Self 9 0.38 0.71 0.605 0.39 1.5
## angry_Self 4 -0.13 0.70 0.529 0.47 1.1
## grumpy_Self 24 -0.23 0.66 0.513 0.49 1.2
## controlling_Self 15 0.43 0.64 0.553 0.45 1.8
## considerate_Self 14 0.15 -0.57 0.361 0.64 1.1
## patient_Self 35 0.21 -0.56 0.376 0.62 1.3
## lazy_Self 30 -0.06 0.53 0.286 0.71 1.0
## humble_Self 27 -0.08 -0.53 0.275 0.73 1.0
## jealous_Self 29 -0.21 0.52 0.327 0.67 1.3
## calm_Self 10 0.31 -0.50 0.375 0.63 1.7
## genuine_Self 22 0.25 -0.48 0.318 0.68 1.5
## helpful_Self 25 0.38 -0.48 0.404 0.60 1.9
## poor_Self 37 -0.43 0.47 0.445 0.55 2.0
## caring_Self 11 0.32 -0.47 0.344 0.66 1.8
## honest_Self 26 0.35 -0.45 0.350 0.65 1.9
## risky_Self 40 0.34 0.45 0.292 0.71 1.9
## giving_Self 23 0.31 -0.42 0.294 0.71 1.8
## stubborn_Self 46 0.12 0.38 0.152 0.85 1.2
## rule-follower_Self 41 -0.03 -0.34 0.118 0.88 1.0
## studious_Self 47 0.06 -0.32 0.113 0.89 1.1
## dependent_Self 18 -0.09 0.23 0.065 0.94 1.3
##
## PA1 PA2
## SS loadings 12.95 7.89
## Proportion Var 0.27 0.16
## Cumulative Var 0.27 0.43
## Proportion Explained 0.62 0.38
## Cumulative Proportion 0.62 1.00
##
## With factor correlations of
## PA1 PA2
## PA1 1.00 -0.09
## PA2 -0.09 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 1128 and the objective function was 46.46 with Chi Square of 3817.36
## The degrees of freedom for the model are 1033 and the objective function was 23.05
##
## The root mean square of the residuals (RMSR) is 0.09
## The df corrected root mean square of the residuals is 0.1
##
## The harmonic number of observations is 99 with the empirical chi square 1971.92 with prob < 2.7e-61
## The total number of observations was 100 with MLE Chi Square = 1862.85 with prob < 2.5e-50
##
## Tucker Lewis Index of factoring reliability = 0.655
## RMSEA index = 0.11 and the 90 % confidence intervals are 0.083 0.096
## BIC = -2894.29
## Fit based upon off diagonal values = 0.92
## Measures of factor score adequacy
## PA1 PA2
## Correlation of scores with factors 0.99 0.97
## Multiple R square of scores with factors 0.97 0.94
## Minimum correlation of possible factor scores 0.94 0.88
## Factor Analysis using method = pa
## Call: fa(r = select(selfRateDat_lim, -matches("SelfPop")), nfactors = 4,
## rotate = "oblimin", scores = "tenBerge", fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PA1 PA3 PA2 PA4 h2 u2 com
## insecure_Self 28 0.91 0.08 0.07 0.07 0.76 0.24 1.0
## depressed_Self 19 0.90 0.07 0.13 0.14 0.74 0.26 1.1
## lonely_Self 32 0.83 0.11 0.20 -0.03 0.69 0.31 1.2
## awkward_Self 7 0.81 0.13 0.16 0.05 0.62 0.38 1.1
## confident_Self 13 -0.76 0.21 0.22 0.02 0.77 0.23 1.3
## trendy_Self 48 -0.75 0.05 0.33 0.03 0.72 0.28 1.4
## loner_Self 33 0.74 -0.04 0.06 -0.12 0.64 0.36 1.1
## popular_Self 38 -0.67 0.23 0.27 0.11 0.74 0.26 1.7
## plain_Self 36 0.64 0.11 0.11 -0.11 0.44 0.56 1.2
## shy_Self 43 0.61 0.22 0.05 -0.30 0.52 0.48 1.8
## social_Self 45 -0.59 0.22 0.19 0.27 0.72 0.28 2.0
## outgoing_Self 34 -0.55 0.14 0.22 0.16 0.52 0.48 1.7
## boring _Self 8 0.54 -0.05 0.28 -0.22 0.48 0.52 1.9
## flirty_Self 20 -0.53 0.04 0.22 0.24 0.51 0.49 1.8
## cool_Self 16 -0.52 0.31 0.41 0.12 0.70 0.30 2.7
## admired_Self 1 -0.52 0.28 0.34 0.18 0.66 0.34 2.6
## leader_Self 31 -0.51 0.15 0.34 0.09 0.50 0.50 2.0
## poor_Self 37 0.51 -0.24 0.24 0.10 0.46 0.54 2.0
## pushover_Self 39 0.50 0.02 0.25 -0.15 0.35 0.65 1.7
## attractive_Self 6 -0.46 0.34 0.10 0.31 0.63 0.37 2.8
## funny_Self 21 -0.35 0.30 0.00 0.32 0.45 0.55 3.0
## athletic_Self 5 -0.25 0.23 0.09 0.08 0.18 0.82 2.5
## helpful_Self 25 0.02 0.84 -0.08 0.15 0.75 0.25 1.1
## considerate_Self 14 0.17 0.83 -0.16 0.02 0.69 0.31 1.2
## caring_Self 11 0.04 0.75 -0.13 0.15 0.61 0.39 1.2
## genuine_Self 22 -0.01 0.75 0.00 -0.11 0.57 0.43 1.0
## giving_Self 23 -0.01 0.70 -0.05 0.06 0.50 0.50 1.0
## humble_Self 27 0.21 0.61 -0.18 -0.13 0.43 0.57 1.5
## calm_Self 10 -0.25 0.57 -0.01 -0.26 0.50 0.50 1.8
## honest_Self 26 -0.24 0.48 -0.12 -0.05 0.39 0.61 1.6
## patient_Self 35 -0.21 0.48 -0.18 -0.19 0.41 0.59 2.0
## comforting_Self 12 -0.32 0.45 -0.02 0.04 0.40 0.60 1.8
## studious_Self 47 -0.03 0.42 0.07 -0.28 0.24 0.76 1.8
## controlling_Self 15 -0.19 -0.03 0.76 0.06 0.66 0.34 1.1
## snobby_Self 44 0.00 -0.28 0.75 0.01 0.69 0.31 1.3
## bossy_Self 9 -0.14 -0.15 0.68 0.17 0.63 0.37 1.3
## agressive_Self 3 -0.06 -0.25 0.63 0.12 0.56 0.44 1.4
## angry_Self 4 0.39 -0.12 0.61 0.13 0.63 0.37 1.9
## grumpy_Self 24 0.47 -0.09 0.60 0.08 0.64 0.36 2.0
## jealous_Self 29 0.39 -0.05 0.50 0.01 0.43 0.57 1.9
## lazy_Self 30 0.16 -0.15 0.50 -0.03 0.33 0.67 1.4
## selfish_Self 42 0.20 -0.30 0.49 0.20 0.51 0.49 2.5
## dependent_Self 18 0.20 0.15 0.45 -0.19 0.23 0.77 2.0
## stubborn_Self 46 0.19 0.08 0.34 0.26 0.24 0.76 2.6
## daring_Self 17 -0.10 0.11 0.04 0.72 0.63 0.37 1.1
## risky_Self 40 0.11 -0.01 0.16 0.68 0.53 0.47 1.2
## rule-follower_Self 41 -0.05 0.45 0.21 -0.57 0.45 0.55 2.2
## adventurous_Self 2 -0.27 0.31 0.11 0.49 0.60 0.40 2.5
##
## PA1 PA3 PA2 PA4
## SS loadings 10.78 6.48 5.46 3.31
## Proportion Var 0.22 0.14 0.11 0.07
## Cumulative Var 0.22 0.36 0.47 0.54
## Proportion Explained 0.41 0.25 0.21 0.13
## Cumulative Proportion 0.41 0.66 0.87 1.00
##
## With factor correlations of
## PA1 PA3 PA2 PA4
## PA1 1.00 -0.31 -0.01 -0.30
## PA3 -0.31 1.00 -0.10 0.04
## PA2 -0.01 -0.10 1.00 0.34
## PA4 -0.30 0.04 0.34 1.00
##
## Mean item complexity = 1.7
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 1128 and the objective function was 46.46 with Chi Square of 3817.36
## The degrees of freedom for the model are 942 and the objective function was 16.73
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.06
##
## The harmonic number of observations is 99 with the empirical chi square 573.57 with prob < 1
## The total number of observations was 100 with MLE Chi Square = 1329.86 with prob < 9e-16
##
## Tucker Lewis Index of factoring reliability = 0.819
## RMSEA index = 0.088 and the 90 % confidence intervals are 0.056 0.072
## BIC = -3008.22
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy
## PA1 PA3 PA2 PA4
## Correlation of scores with factors 0.98 0.97 0.97 0.93
## Multiple R square of scores with factors 0.97 0.94 0.94 0.86
## Minimum correlation of possible factor scores 0.94 0.88 0.87 0.73
These clusters of items may still be related to status (and they’re actually pretty close to the expected factors, just divided up a bit more). We can correlate self rated accepted and controversial status with the factor scores to start exploring this.
In the output below, SelfPop_1 is controversial, and SelfPop_2 is accepted.
Also:
We see that controversial status is correlated with aggression and with risk-taking.
We see accepted status is highly correlated with the surgency/dynamism component (remember, reverse the sign here because of the depression item anchoring the scale).
## Call:corr.test(x = as.data.frame(selfPopDat), y = as.data.frame(predict(selfRateFA,
## selfRateDat_nopop_imputed, missing = T, use = "pairwise.complete.obs")),
## use = "pairwise.complete.obs", adjust = "none")
## Correlation matrix
## V1 V2 V3 V4
## SelfPop_1 0.05 -0.18 0.52 0.22
## SelfPop_2 -0.71 0.16 0.14 0.10
## Sample Size
## V1 V2 V3 V4
## SelfPop_1 98 98 98 98
## SelfPop_2 100 100 100 100
## V1 V2 V3 V4
## SelfPop_1 0.6 0.08 0.00 0.03
## SelfPop_2 0.0 0.12 0.17 0.33
##
## To see confidence intervals of the correlations, print with the short=FALSE option
Grain of salt: No correction for multiple comparison here.
Slightly bigger grain of salt: 8 folks are missing a rating on a couple items here and there, so I impute the mean so we can get predicted factor scores. This means that significance values and CIs close to threshold below should be treated lightly (but it doesn’t change things too much).
This gets more interesting in the regressions.
Here’s the raw output for regressing controversial status on the component scores – see below for a table with CIs.
##
## Call: rlm(formula = selfPopDat[, c("SelfPop_1")] ~ predict(selfRateFA,
## selfRateDat_nopop_imputed))
## Residuals:
## Min 1Q Median 3Q Max
## -3.02969 -0.63801 -0.06832 0.71037 3.75564
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 2.3128 0.1243 18.6025
## predict(selfRateFA, selfRateDat_nopop_imputed)1 0.0440 0.1248 0.3527
## predict(selfRateFA, selfRateDat_nopop_imputed)2 -0.3489 0.1248 -2.7956
## predict(selfRateFA, selfRateDat_nopop_imputed)3 0.9388 0.1246 7.5343
## predict(selfRateFA, selfRateDat_nopop_imputed)4 0.2658 0.1250 2.1259
##
## Residual standard error: 0.977 on 93 degrees of freedom
## (2 observations deleted due to missingness)
Results from bootstrap estimates: Controversial status is significantly predicted by lower prosocial scores (2), and higher aggression scores (3). Estimates for risk-taking (4) is positive and just past threshold.
| component | est | lower 95% | upper 95% |
|---|---|---|---|
| 1 | 0.04 | -0.18 | 0.31 |
| 2 | -0.35 | -0.67 | -0.09 |
| 3 | 0.94 | 0.61 | 1.23 |
| 4 | 0.27 | 0.01 | 0.70 |
Here’s the raw output for an rlm of accepted status on the component scores. Again, scroll down for a nice table.
##
## Call: rlm(formula = selfPopDat[, c("SelfPop_2")] ~ predict(selfRateFA,
## selfRateDat_nopop_imputed))
## Residuals:
## Min 1Q Median 3Q Max
## -3.457979 -0.571774 0.003142 0.579391 2.649151
##
## Coefficients:
## Value Std. Error
## (Intercept) 3.5265 0.1042
## predict(selfRateFA, selfRateDat_nopop_imputed)1 -1.2461 0.1048
## predict(selfRateFA, selfRateDat_nopop_imputed)2 0.2824 0.1048
## predict(selfRateFA, selfRateDat_nopop_imputed)3 0.3293 0.1048
## predict(selfRateFA, selfRateDat_nopop_imputed)4 0.1719 0.1047
## t value
## (Intercept) 33.8405
## predict(selfRateFA, selfRateDat_nopop_imputed)1 -11.8864
## predict(selfRateFA, selfRateDat_nopop_imputed)2 2.6959
## predict(selfRateFA, selfRateDat_nopop_imputed)3 3.1418
## predict(selfRateFA, selfRateDat_nopop_imputed)4 1.6424
##
## Residual standard error: 0.8548 on 95 degrees of freedom
Accepted status is significantly predicted by higher surgency (1; remember, flip the sign), and prosocial scores (2). Interestingly aggression (3) is also significant.
| component | est | lower 95% | upper 95% |
|---|---|---|---|
| 1 | -1.25 | -1.44 | -1.00 |
| 2 | 0.28 | 0.08 | 0.49 |
| 3 | 0.33 | 0.06 | 0.57 |
| 4 | 0.17 | -0.11 | 0.42 |
Well, we have four factors that are helpfully related to self reported status. This is what we want. All four factors seem relevant.
Now we need a principled way to select items. We could use some communality cutoff, or loading strength. But we know we want 48 items, so let’s start there. We can use regularized regression methods to let the machine learn what 48 items give us the best set of factors. We can then compare that to the EFA results as well as to the earlier classification.
## iterations 10
## iterations 20
## iterations 30
## iterations 10
## iterations 20
## iterations 30
## iterations 10
## iterations 20
## iterations 30
## iterations 10
## iterations 20
## iterations 30
## iterations 10
## iterations 20
## iterations 10
## iterations 20
## iterations 30
## [[1]]
## para Nitems
## 1 44
##
## [[2]]
## para Nitems
## 1.2 44.0
##
## [[3]]
## para Nitems
## 1.4 43.0
##
## [[4]]
## para Nitems
## 1.6 40.0
##
## [[5]]
## para Nitems
## 1.8 36.0
##
## [[6]]
## para Nitems
## 2 32
A penalty parameter of 1.4 (#3) gives us the number of items we want (48 unique).
| PC1 | PC2 | PC3 | PC4 | |
|---|---|---|---|---|
| admired_Self | -0.092 | |||
| adventurous_Self | 0.248 | |||
| agressive_Self | 0.176 | |||
| angry_Self | 0.395 | |||
| athletic_Self | ||||
| attractive_Self | -0.178 | |||
| awkward_Self | 0.287 | |||
| boring _Self | 0.045 | |||
| bossy_Self | 0.498 | |||
| calm_Self | 0.195 | |||
| caring_Self | ||||
| comforting_Self | 0.022 | |||
| confident_Self | -0.346 | |||
| considerate_Self | 0.335 | |||
| controlling_Self | 0.394 | |||
| cool_Self | -0.123 | |||
| daring_Self | 0.78 | |||
| dependent_Self | ||||
| depressed_Self | 0.3 | |||
| flirty_Self | -0.003 | |||
| funny_Self | ||||
| genuine_Self | 0.362 | |||
| giving_Self | 0.435 | |||
| grumpy_Self | 0.308 | |||
| helpful_Self | 0.637 | |||
| honest_Self | ||||
| humble_Self | 0.176 | |||
| insecure_Self | 0.439 | |||
| jealous_Self | 0.105 | |||
| lazy_Self | 0.071 | |||
| leader_Self | -0.096 | |||
| lonely_Self | 0.221 | |||
| loner_Self | 0.35 | |||
| outgoing_Self | -0.141 | |||
| patient_Self | 0.1 | |||
| plain_Self | 0.047 | |||
| poor_Self | 0.025 | |||
| popular_Self | -0.328 | |||
| pushover_Self | 0.031 | |||
| risky_Self | 0.574 | |||
| rule-follower_Self | 0.266 | |||
| selfish_Self | 0.065 | |||
| shy_Self | 0.165 | |||
| snobby_Self | 0.541 | |||
| social_Self | -0.317 | |||
| stubborn_Self | 0.049 | |||
| studious_Self | 0.111 | |||
| trendy_Self | -0.137 |
The next obvious step is to look and see what a regular EFA tells us about this selection of items
Whammo, 4 factors again.
## Factor Analysis using method = pa
## Call: fa(r = eItemDF, nfactors = 4, rotate = "oblimin", scores = "tenBerge",
## fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item PA1 PA3 PA2 PA4 h2 u2 com
## depressed_Self 16 0.90 0.04 0.08 0.16 0.74 0.26 1.1
## insecure_Self 23 0.90 0.06 0.06 0.03 0.76 0.24 1.0
## lonely_Self 27 0.84 0.11 0.17 -0.04 0.70 0.30 1.1
## awkward_Self 6 0.82 0.13 0.14 0.05 0.62 0.38 1.1
## loner_Self 28 0.74 -0.05 0.04 -0.14 0.65 0.35 1.1
## trendy_Self 43 -0.73 0.07 0.36 0.01 0.72 0.28 1.5
## confident_Self 11 -0.71 0.24 0.23 0.06 0.77 0.23 1.5
## plain_Self 31 0.65 0.13 0.09 -0.12 0.45 0.55 1.2
## popular_Self 33 -0.63 0.25 0.28 0.14 0.74 0.26 1.9
## shy_Self 38 0.62 0.21 -0.02 -0.24 0.50 0.50 1.5
## boring _Self 7 0.59 -0.01 0.23 -0.16 0.45 0.55 1.5
## social_Self 40 -0.57 0.21 0.20 0.29 0.72 0.28 2.1
## pushover_Self 34 0.53 0.04 0.22 -0.13 0.35 0.65 1.5
## poor_Self 32 0.53 -0.25 0.23 0.09 0.47 0.53 1.9
## flirty_Self 17 -0.51 0.01 0.21 0.28 0.52 0.48 1.9
## outgoing_Self 29 -0.51 0.15 0.21 0.21 0.52 0.48 1.9
## leader_Self 26 -0.48 0.18 0.38 0.08 0.51 0.49 2.3
## cool_Self 14 -0.47 0.34 0.40 0.18 0.71 0.29 3.1
## admired_Self 1 -0.47 0.30 0.34 0.21 0.67 0.33 3.1
## attractive_Self 5 -0.43 0.32 0.11 0.33 0.62 0.38 2.9
## considerate_Self 12 0.17 0.80 -0.21 0.08 0.66 0.34 1.3
## helpful_Self 21 0.04 0.79 -0.14 0.23 0.71 0.29 1.2
## genuine_Self 18 0.00 0.74 -0.02 -0.07 0.55 0.45 1.0
## giving_Self 19 0.01 0.67 -0.10 0.13 0.49 0.51 1.1
## calm_Self 9 -0.22 0.63 -0.01 -0.22 0.52 0.48 1.5
## humble_Self 22 0.22 0.61 -0.20 -0.10 0.43 0.57 1.6
## patient_Self 30 -0.17 0.50 -0.24 -0.08 0.42 0.58 1.8
## studious_Self 42 -0.02 0.46 0.06 -0.27 0.25 0.75 1.7
## comforting_Self 10 -0.29 0.45 -0.03 0.09 0.41 0.59 1.8
## controlling_Self 13 -0.16 -0.01 0.79 0.02 0.67 0.33 1.1
## bossy_Self 8 -0.11 -0.13 0.72 0.12 0.64 0.36 1.2
## snobby_Self 39 0.07 -0.24 0.72 0.06 0.65 0.35 1.3
## agressive_Self 3 -0.03 -0.23 0.66 0.09 0.57 0.43 1.3
## angry_Self 4 0.40 -0.12 0.62 0.09 0.63 0.37 1.9
## grumpy_Self 20 0.49 -0.08 0.61 0.03 0.64 0.36 2.0
## selfish_Self 37 0.20 -0.32 0.49 0.16 0.51 0.49 2.3
## lazy_Self 25 0.19 -0.14 0.48 -0.01 0.32 0.68 1.5
## jealous_Self 24 0.43 -0.04 0.47 0.03 0.41 0.59 2.0
## stubborn_Self 41 0.19 0.09 0.38 0.20 0.24 0.76 2.2
## daring_Self 15 -0.06 0.05 -0.01 0.82 0.71 0.29 1.0
## risky_Self 35 0.12 -0.07 0.17 0.67 0.52 0.48 1.2
## adventurous_Self 2 -0.23 0.28 0.08 0.56 0.62 0.38 1.9
## rule-follower_Self 36 -0.02 0.53 0.20 -0.53 0.45 0.55 2.3
##
## PA1 PA3 PA2 PA4
## SS loadings 10.11 5.43 5.37 3.27
## Proportion Var 0.24 0.13 0.12 0.08
## Cumulative Var 0.24 0.36 0.49 0.56
## Proportion Explained 0.42 0.22 0.22 0.14
## Cumulative Proportion 0.42 0.64 0.86 1.00
##
## With factor correlations of
## PA1 PA3 PA2 PA4
## PA1 1.00 -0.31 -0.02 -0.31
## PA3 -0.31 1.00 -0.11 0.09
## PA2 -0.02 -0.11 1.00 0.35
## PA4 -0.31 0.09 0.35 1.00
##
## Mean item complexity = 1.7
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 903 and the objective function was 40.07 with Chi Square of 3359.29
## The degrees of freedom for the model are 737 and the objective function was 12.6
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 99 with the empirical chi square 422.8 with prob < 1
## The total number of observations was 100 with MLE Chi Square = 1022.96 with prob < 1.2e-11
##
## Tucker Lewis Index of factoring reliability = 0.851
## RMSEA index = 0.084 and the 90 % confidence intervals are 0.053 0.071
## BIC = -2371.05
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy
## PA1 PA3 PA2 PA4
## Correlation of scores with factors 0.98 0.96 0.97 0.93
## Multiple R square of scores with factors 0.97 0.92 0.93 0.87
## Minimum correlation of possible factor scores 0.93 0.85 0.87 0.75
| item | PA1 | PA3 | PA2 | PA4 | comm |
|---|---|---|---|---|---|
| depressed_Self | 0.90 | 0.16 | 0.74 | ||
| insecure_Self | 0.90 | 0.76 | |||
| lonely_Self | 0.84 | 0.11 | 0.17 | 0.70 | |
| awkward_Self | 0.82 | 0.13 | 0.14 | 0.62 | |
| loner_Self | 0.74 | -0.14 | 0.65 | ||
| trendy_Self | -0.73 | 0.36 | 0.72 | ||
| confident_Self | -0.71 | 0.24 | 0.23 | 0.77 | |
| plain_Self | 0.65 | 0.13 | -0.12 | 0.45 | |
| popular_Self | -0.63 | 0.25 | 0.28 | 0.14 | 0.74 |
| shy_Self | 0.62 | 0.21 | -0.24 | 0.50 | |
| boring _Self | 0.59 | 0.23 | -0.16 | 0.45 | |
| social_Self | -0.57 | 0.21 | 0.20 | 0.29 | 0.72 |
| pushover_Self | 0.53 | 0.22 | -0.13 | 0.35 | |
| poor_Self | 0.53 | -0.25 | 0.23 | 0.47 | |
| flirty_Self | -0.51 | 0.21 | 0.28 | 0.52 | |
| outgoing_Self | -0.51 | 0.15 | 0.21 | 0.21 | 0.52 |
| leader_Self | -0.48 | 0.18 | 0.38 | 0.51 | |
| cool_Self | -0.47 | 0.34 | 0.40 | 0.18 | 0.71 |
| admired_Self | -0.47 | 0.30 | 0.34 | 0.21 | 0.67 |
| attractive_Self | -0.43 | 0.32 | 0.11 | 0.33 | 0.62 |
| considerate_Self | 0.17 | 0.80 | -0.21 | 0.66 | |
| helpful_Self | 0.79 | -0.14 | 0.23 | 0.71 | |
| genuine_Self | 0.74 | 0.55 | |||
| giving_Self | 0.67 | -0.10 | 0.13 | 0.49 | |
| calm_Self | -0.22 | 0.63 | -0.22 | 0.52 | |
| humble_Self | 0.22 | 0.61 | -0.20 | -0.10 | 0.43 |
| patient_Self | -0.17 | 0.50 | -0.24 | 0.42 | |
| studious_Self | 0.46 | -0.27 | 0.25 | ||
| comforting_Self | -0.29 | 0.45 | 0.41 | ||
| controlling_Self | -0.16 | 0.79 | 0.67 | ||
| bossy_Self | -0.11 | -0.13 | 0.72 | 0.12 | 0.64 |
| snobby_Self | -0.24 | 0.72 | 0.65 | ||
| agressive_Self | -0.23 | 0.66 | 0.57 | ||
| angry_Self | 0.40 | -0.12 | 0.62 | 0.63 | |
| grumpy_Self | 0.49 | 0.61 | 0.64 | ||
| selfish_Self | 0.20 | -0.32 | 0.49 | 0.16 | 0.51 |
| lazy_Self | 0.19 | -0.14 | 0.48 | 0.32 | |
| jealous_Self | 0.43 | 0.47 | 0.41 | ||
| stubborn_Self | 0.19 | 0.38 | 0.20 | 0.24 | |
| daring_Self | 0.82 | 0.71 | |||
| risky_Self | 0.12 | 0.17 | 0.67 | 0.52 | |
| adventurous_Self | -0.23 | 0.28 | 0.56 | 0.62 | |
| rule-follower_Self | 0.53 | 0.20 | -0.53 | 0.45 |
For reference, the original EFA with items that also appear above in bold.
| item | PA3 | PA1 | PA2 | PA4 | comm |
|---|---|---|---|---|---|
| depressed_Self | 0.91 | 0.11 | 0.16 | 0.16 | 0.758 |
| insecure_Self | 0.89 | 0.10 | 0.745 | ||
| lonely_Self | 0.83 | 0.13 | 0.23 | 0.692 | |
| awkward_Self | 0.83 | 0.16 | 0.16 | 0.620 | |
| trendy_Self | -0.76 | 0.33 | 0.715 | ||
| confident_Self | -0.76 | 0.21 | 0.21 | 0.762 | |
| loner_Self | 0.74 | -0.12 | 0.642 | ||
| popular_Self | -0.69 | 0.24 | 0.30 | 0.743 | |
| plain_Self | 0.66 | 0.424 | |||
| shy_Self | 0.62 | 0.19 | -0.28 | 0.506 | |
| social_Self | -0.60 | 0.25 | 0.21 | 0.27 | 0.720 |
| boring_Self | 0.57 | 0.27 | -0.19 | 0.479 | |
| outgoing_Self | -0.56 | 0.17 | 0.23 | 0.14 | 0.517 |
| flirty_Self | -0.55 | 0.24 | 0.21 | 0.508 | |
| admired_Self | -0.55 | 0.27 | 0.34 | 0.17 | 0.653 |
| cool_Self | -0.54 | 0.29 | 0.41 | 0.12 | 0.680 |
| leader_Self | -0.54 | 0.13 | 0.34 | 0.495 | |
| ugly_Self | 0.53 | -0.20 | 0.19 | -0.14 | 0.479 |
| pushover_Self | 0.52 | 0.24 | -0.14 | 0.352 | |
| poor_Self | 0.50 | -0.22 | 0.26 | 0.459 | |
| attractive_Self | -0.50 | 0.36 | 0.15 | 0.26 | 0.641 |
| funny_Self | -0.37 | 0.33 | 0.28 | 0.454 | |
| athletic_Self | -0.28 | 0.20 | 0.171 | ||
| nice_Self | 0.85 | -0.16 | 0.743 | ||
| considerate_Self | 0.18 | 0.84 | -0.15 | 0.699 | |
| helpful_Self | 0.81 | 0.15 | 0.689 | ||
| caring_Self | 0.77 | 0.14 | 0.625 | ||
| genuine_Self | 0.76 | -0.14 | 0.590 | ||
| loyal_Self | 0.73 | -0.11 | 0.514 | ||
| trustworthy_Self | 0.73 | 0.10 | 0.597 | ||
| friendly_Self | -0.11 | 0.72 | 0.591 | ||
| giving_Self | 0.71 | 0.516 | |||
| sympathetic_Self | 0.71 | 0.520 | |||
| welcoming_Self | 0.69 | -0.18 | 0.590 | ||
| fair_Self | 0.59 | -0.18 | 0.456 | ||
| humble_Self | 0.21 | 0.55 | -0.18 | -0.13 | 0.382 |
| respectful_Self | -0.17 | 0.55 | 0.13 | -0.44 | 0.508 |
| calm_Self | -0.22 | 0.54 | -0.19 | 0.460 | |
| honest_Self | -0.24 | 0.49 | -0.11 | 0.403 | |
| smart_Self | 0.46 | -0.12 | 0.243 | ||
| motivated_Self | -0.25 | 0.44 | -0.25 | 0.348 | |
| studious_Self | 0.44 | -0.34 | 0.296 | ||
| comforting_Self | -0.34 | 0.44 | 0.397 | ||
| patient_Self | -0.18 | 0.42 | -0.22 | -0.12 | 0.362 |
| mean_Self | -0.32 | 0.75 | 0.722 | ||
| controlling_Self | -0.19 | 0.74 | 0.631 | ||
| snobby_Self | -0.28 | 0.73 | 0.701 | ||
| rude_Self | -0.25 | 0.72 | 0.650 | ||
| bossy_Self | -0.17 | -0.12 | 0.70 | 0.13 | 0.623 |
| angry_Self | 0.38 | 0.65 | 0.12 | 0.640 | |
| grumpy_Self | 0.46 | 0.62 | 0.623 | ||
| agressive_Self | -0.23 | 0.61 | 0.17 | 0.553 | |
| selfish_Self | 0.17 | -0.26 | 0.54 | 0.17 | 0.522 |
| jealous_Self | 0.42 | 0.52 | 0.439 | ||
| lazy_Self | 0.17 | -0.16 | 0.48 | 0.331 | |
| fake_Self | 0.16 | -0.40 | 0.47 | 0.515 | |
| dependent_Self | 0.22 | 0.16 | 0.45 | -0.17 | 0.235 |
| stubborn_Self | 0.16 | 0.14 | 0.37 | 0.22 | 0.224 |
| daring_Self | -0.15 | 0.15 | 0.13 | 0.67 | 0.616 |
| risky_Self | 0.22 | 0.63 | 0.503 | ||
| rule-follower_Self | 0.44 | 0.20 | -0.59 | 0.492 | |
| adventurous_Self | -0.31 | 0.34 | 0.17 | 0.45 | 0.596 |
We could also pick items based on cross loadings (minimizing) and communality (maximizing).
| item | max | maxPA | ssXload | comm | scalemax | scalessX | scalecomm | crit |
|---|---|---|---|---|---|---|---|---|
| athletic_Self | -0.25 | PA1 | 0.07 | 0.18 | -2.33 | 0.41 | -2.35 | -1.42 |
| funny_Self | -0.35 | PA1 | 0.19 | 0.45 | -1.73 | -1.24 | -0.59 | -1.19 |
| attractive_Self | -0.46 | PA1 | 0.22 | 0.63 | -1.00 | -1.49 | 0.57 | -0.64 |
| pushover_Self | 0.50 | PA1 | 0.09 | 0.35 | -0.69 | 0.10 | -1.27 | -0.62 |
| leader_Self | -0.51 | PA1 | 0.15 | 0.50 | -0.63 | -0.75 | -0.26 | -0.54 |
| poor_Self | 0.51 | PA1 | 0.13 | 0.46 | -0.64 | -0.44 | -0.55 | -0.54 |
| cool_Self | -0.52 | PA1 | 0.28 | 0.70 | -0.55 | -2.02 | 1.05 | -0.50 |
| boring_Self | 0.54 | PA1 | 0.13 | 0.48 | -0.43 | -0.54 | -0.44 | -0.47 |
| admired_Self | -0.52 | PA1 | 0.22 | 0.66 | -0.57 | -1.52 | 0.80 | -0.43 |
| flirty_Self | -0.53 | PA1 | 0.11 | 0.51 | -0.53 | -0.21 | -0.20 | -0.31 |
| shy_Self | 0.61 | PA1 | 0.14 | 0.52 | 0.05 | -0.65 | -0.12 | -0.24 |
| outgoing_Self | -0.55 | PA1 | 0.09 | 0.52 | -0.39 | 0.00 | -0.17 | -0.19 |
| social_Self | -0.59 | PA1 | 0.16 | 0.72 | -0.11 | -0.85 | 1.15 | 0.07 |
| plain_Self | 0.64 | PA1 | 0.04 | 0.44 | 0.24 | 1.05 | -0.69 | 0.20 |
| popular_Self | -0.67 | PA1 | 0.14 | 0.74 | 0.40 | -0.61 | 1.27 | 0.35 |
| trendy_Self | -0.75 | PA1 | 0.11 | 0.72 | 0.97 | -0.25 | 1.18 | 0.63 |
| confident_Self | -0.76 | PA1 | 0.09 | 0.77 | 1.00 | 0.03 | 1.48 | 0.83 |
| awkward_Self | 0.81 | PA1 | 0.05 | 0.62 | 1.37 | 0.86 | 0.50 | 0.91 |
| loner_Self | 0.74 | PA1 | 0.02 | 0.64 | 0.89 | 1.51 | 0.62 | 1.01 |
| lonely_Self | 0.83 | PA1 | 0.05 | 0.69 | 1.47 | 0.70 | 0.96 | 1.04 |
| depressed_Self | 0.90 | PA1 | 0.04 | 0.74 | 1.91 | 0.96 | 1.32 | 1.39 |
| insecure_Self | 0.91 | PA1 | 0.02 | 0.76 | 2.00 | 1.67 | 1.45 | 1.71 |
| stubborn_Self | 0.34 | PA2 | 0.11 | 0.24 | -1.79 | -0.22 | -1.99 | -1.33 |
| dependent_Self | 0.45 | PA2 | 0.10 | 0.23 | -1.01 | -0.08 | -2.04 | -1.04 |
| jealous_Self | 0.50 | PA2 | 0.16 | 0.43 | -0.68 | -0.81 | -0.77 | -0.75 |
| selfish_Self | 0.49 | PA2 | 0.17 | 0.51 | -0.80 | -0.98 | -0.21 | -0.66 |
| lazy_Self | 0.50 | PA2 | 0.05 | 0.33 | -0.68 | 0.78 | -1.41 | -0.44 |
| grumpy_Self | 0.60 | PA2 | 0.23 | 0.64 | -0.06 | -1.65 | 0.62 | -0.36 |
| angry_Self | 0.61 | PA2 | 0.19 | 0.63 | 0.03 | -1.15 | 0.54 | -0.19 |
| agressive_Self | 0.63 | PA2 | 0.08 | 0.56 | 0.18 | 0.18 | 0.15 | 0.17 |
| bossy_Self | 0.68 | PA2 | 0.07 | 0.63 | 0.50 | 0.37 | 0.61 | 0.49 |
| snobby_Self | 0.75 | PA2 | 0.08 | 0.69 | 0.95 | 0.26 | 0.97 | 0.73 |
| controlling_Self | 0.76 | PA2 | 0.04 | 0.66 | 1.00 | 0.92 | 0.76 | 0.90 |
| studious_Self | 0.42 | PA3 | 0.08 | 0.24 | -1.22 | 0.15 | -2.01 | -1.03 |
| comforting_Self | 0.45 | PA3 | 0.10 | 0.40 | -1.06 | -0.12 | -0.94 | -0.71 |
| patient_Self | 0.48 | PA3 | 0.11 | 0.41 | -0.83 | -0.25 | -0.84 | -0.64 |
| honest_Self | 0.48 | PA3 | 0.08 | 0.39 | -0.82 | 0.30 | -1.02 | -0.51 |
| calm_Self | 0.57 | PA3 | 0.13 | 0.50 | -0.21 | -0.51 | -0.26 | -0.33 |
| humble_Self | 0.61 | PA3 | 0.09 | 0.43 | -0.01 | -0.01 | -0.74 | -0.25 |
| caring_Self | 0.75 | PA3 | 0.04 | 0.61 | 0.98 | 0.90 | 0.43 | 0.77 |
| giving_Self | 0.70 | PA3 | 0.01 | 0.50 | 0.58 | 2.09 | -0.26 | 0.80 |
| genuine_Self | 0.75 | PA3 | 0.01 | 0.57 | 0.94 | 1.79 | 0.20 | 0.98 |
| considerate_Self | 0.83 | PA3 | 0.06 | 0.69 | 1.49 | 0.64 | 0.95 | 1.03 |
| helpful_Self | 0.84 | PA3 | 0.03 | 0.75 | 1.57 | 1.24 | 1.34 | 1.38 |
| rule-follower_Self | -0.57 | PA4 | 0.25 | 0.45 | -0.24 | -1.79 | -0.62 | -0.88 |
| adventurous_Self | 0.49 | PA4 | 0.19 | 0.60 | -0.80 | -1.15 | 0.36 | -0.53 |
| risky_Self | 0.68 | PA4 | 0.04 | 0.53 | 0.46 | 1.06 | -0.11 | 0.47 |
| daring_Self | 0.72 | PA4 | 0.03 | 0.63 | 0.77 | 1.35 | 0.56 | 0.89 |
Based on this table, we could drop items with low scores on ‘crit’, which is just an average of Z scores for each of our criteria (main factor loading, cross-loadings, and communality). I can’t think of a principled way to do this, and given the imbalance already in the number of items, we can’t really set an arbitrary number per factor.
I’m going to set this route aside for no, because the SPCA item selection seems fine for now, especially if we get good prediction below. (The basis behind SPCA is the same as PCA/EFA, which is is to identify loadings on factors that capture the maximum amount of variance in the data. In light of that, the 48 items should do what we want).
##
## Call: rlm(formula = selfPopDat[, c("SelfPop_1")] ~ predict(eItemFA,
## eitemDF_imputed))
## Residuals:
## Min 1Q Median 3Q Max
## -3.04491 -0.65924 -0.03565 0.59240 3.71589
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 2.3116 0.1172 19.7302
## predict(eItemFA, eitemDF_imputed)1 0.0647 0.1177 0.5496
## predict(eItemFA, eitemDF_imputed)2 -0.3350 0.1175 -2.8496
## predict(eItemFA, eitemDF_imputed)3 0.9661 0.1175 8.2228
## predict(eItemFA, eitemDF_imputed)4 0.2297 0.1177 1.9520
##
## Residual standard error: 0.9275 on 93 degrees of freedom
## (2 observations deleted due to missingness)
Results from bootstrap estimates: Controversial status is significantly predicted by lower prosocial scores (2), and higher aggression scores (3). Estimates for risk-taking (4) is positive and just past threshold.
| component | est | lower 95% | upper 95% |
|---|---|---|---|
| 1 | 0.06 | -0.17 | 0.34 |
| 2 | -0.33 | -0.64 | -0.09 |
| 3 | 0.97 | 0.60 | 1.26 |
| 4 | 0.23 | -0.03 | 0.68 |
Here’s the raw output for an rlm of accepted status on the component scores. Again, scroll down for a nice table.
##
## Call: rlm(formula = selfPopDat[, c("SelfPop_2")] ~ predict(eItemFA,
## eitemDF_imputed))
## Residuals:
## Min 1Q Median 3Q Max
## -3.37900 -0.59417 -0.01366 0.65695 2.63990
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 3.5236 0.1069 32.9695
## predict(eItemFA, eitemDF_imputed)1 -1.1987 0.1075 -11.1494
## predict(eItemFA, eitemDF_imputed)2 0.3376 0.1075 3.1414
## predict(eItemFA, eitemDF_imputed)3 0.3617 0.1075 3.3648
## predict(eItemFA, eitemDF_imputed)4 0.2102 0.1074 1.9573
##
## Residual standard error: 0.9656 on 95 degrees of freedom
Accepted status is significantly predicted by higher surgency (1; remember, flip the sign), and prosocial scores (2). Interestingly aggression (3) is also significant.
| component | est | lower 95% | upper 95% |
|---|---|---|---|
| 1 | -1.25 | -1.44 | -1.00 |
| 2 | 0.28 | 0.08 | 0.49 |
| 3 | 0.33 | 0.06 | 0.57 |
| 4 | 0.17 | -0.11 | 0.42 |
Let’s see how this scale works if we just pretend we have a scale.
See raw summary, and below that, tables of bootstrapped CIs.
##
## Call: rlm(formula = SelfPop_1 ~ 1 + admired + adventurous + agressive +
## calm, data = selfRateSPCAScaleScores)
## Residuals:
## Min 1Q Median 3Q Max
## -3.30475 -0.72393 -0.07895 0.70616 3.48107
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.3843 1.3414 1.0319
## admired -0.1857 0.1332 -1.3939
## adventurous -0.0118 0.1463 -0.0809
## agressive 0.9170 0.1409 6.5073
## calm -0.1865 0.1800 -1.0365
##
## Residual standard error: 1.062 on 93 degrees of freedom
## (2 observations deleted due to missingness)
##
## Call: rlm(formula = SelfPop_2 ~ 1 + admired + adventurous + agressive +
## calm, data = selfRateSPCAScaleScores)
## Residuals:
## Min 1Q Median 3Q Max
## -2.848951 -0.555426 0.004171 0.710507 2.765419
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 8.4466 1.2219 6.9128
## admired -1.2445 0.1212 -10.2676
## adventurous -0.3007 0.1322 -2.2746
## agressive 0.1708 0.1280 1.3343
## calm -0.0649 0.1632 -0.3976
##
## Residual standard error: 0.8768 on 95 degrees of freedom
## Call:corr.test(x = select(selfRateSPCAScaleScores, matches("SelfPop")),
## y = select(selfRateSPCAScaleScores, admired, adventurous,
## agressive, calm), use = "pairwise.complete.obs", adjust = "none")
## Correlation matrix
## admired adventurous agressive calm
## SelfPop_1 -0.02 0.28 0.58 -0.28
## SelfPop_2 -0.72 0.20 -0.06 0.22
## Sample Size
## admired adventurous agressive calm
## SelfPop_1 98 98 98 98
## SelfPop_2 100 100 100 100
## admired adventurous agressive calm
## SelfPop_1 0.82 0.01 0.00 0.01
## SelfPop_2 0.00 0.04 0.59 0.03
##
## To see confidence intervals of the correlations, print with the short=FALSE option
| est | lower 95% | upper 95% | |
|---|---|---|---|
| d[, 2:col]admired | -0.19 | -0.44 | 0.19 |
| d[, 2:col]adventurous | -0.01 | -0.34 | 0.52 |
| d[, 2:col]agressive | 0.92 | 0.54 | 1.23 |
| d[, 2:col]calm | -0.19 | -0.61 | 0.16 |
| est | lower 95% | upper 95% | |
|---|---|---|---|
| d[, 2:col]admired | -1.24 | -1.45 | -0.98 |
| d[, 2:col]adventurous | -0.30 | -0.63 | 0.02 |
| d[, 2:col]agressive | 0.17 | -0.12 | 0.41 |
| d[, 2:col]calm | -0.06 | -0.41 | 0.22 |
Ultimately, when we reduce the items to scale scores, only the strongest predictors survive (though note the correlations above). Aggression, all else equal, predicts Controversial High Status. Extraversion, all else equal, predicts accepted status.
## admired=~admired_Self+attractive_Self+awkward_Self+boring_Self+confident_Self+cool_Self+depressed_Self+flirty_Self+insecure_Self+leader_Self+lonely_Self+loner_Self+outgoing_Self+plain_Self+poor_Self+popular_Self+pushover_Self+shy_Self+social_Self+trendy_Self
## agressive=~agressive_Self+angry_Self+bossy_Self+controlling_Self+grumpy_Self+jealous_Self+lazy_Self+selfish_Self+snobby_Self+stubborn_Self
## calm=~calm_Self+comforting_Self+considerate_Self+genuine_Self+giving_Self+helpful_Self+humble_Self+patient_Self+studious_Self
## adventurous=~adventurous_Self+daring_Self+risky_Self+rulefollower_Self
## lavaan (0.5-18) converged normally after 42 iterations
##
## Used Total
## Number of observations 95 100
##
## Estimator ML
## Minimum Function Test Statistic 1844.309
## Degrees of freedom 854
## P-value (Chi-square) 0.000
##
## Model test baseline model:
##
## Minimum Function Test Statistic 3903.054
## Degrees of freedom 903
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.670
## Tucker-Lewis Index (TLI) 0.651
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6315.998
## Loglikelihood unrestricted model (H1) -5393.843
##
## Number of free parameters 92
## Akaike (AIC) 12815.996
## Bayesian (BIC) 13050.952
## Sample-size adjusted Bayesian (BIC) 12760.488
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.110
## 90 Percent Confidence Interval 0.104 0.117
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.147
##
## Parameter estimates:
##
## Information Expected
## Standard Errors Standard
##
## Estimate Std.err Z-value P(>|z|) Std.lv Std.all
## Latent variables:
## admired =~
## admired_Self 1.000 1.122 0.755
## attractiv_Slf 0.888 0.118 7.553 0.000 0.996 0.737
## awkward_Self -1.009 0.148 -6.837 0.000 -1.133 -0.675
## boring_Self -0.802 0.134 -5.992 0.000 -0.900 -0.599
## confident_Slf 1.213 0.133 9.119 0.000 1.361 0.865
## cool_Self 1.008 0.130 7.744 0.000 1.131 0.753
## depressed_Slf -1.114 0.147 -7.577 0.000 -1.250 -0.739
## flirty_Self 1.004 0.143 7.034 0.000 1.127 0.692
## insecure_Self -1.234 0.151 -8.192 0.000 -1.385 -0.790
## leader_Self 0.910 0.136 6.673 0.000 1.022 0.660
## lonely_Self -1.090 0.145 -7.505 0.000 -1.223 -0.733
## loner_Self -1.231 0.147 -8.354 0.000 -1.382 -0.804
## outgoing_Self 1.135 0.153 7.416 0.000 1.273 0.725
## plain_Self -0.879 0.140 -6.268 0.000 -0.987 -0.624
## poor_Self -0.712 0.139 -5.137 0.000 -0.799 -0.520
## popular_Self 1.197 0.136 8.836 0.000 1.344 0.842
## pushover_Self -0.724 0.146 -4.961 0.000 -0.812 -0.503
## shy_Self -0.948 0.152 -6.238 0.000 -1.064 -0.621
## social_Self 1.208 0.137 8.806 0.000 1.355 0.840
## trendy_Self 1.117 0.133 8.431 0.000 1.254 0.810
## agressive =~
## agressive_Slf 1.000 1.053 0.745
## angry_Self 1.073 0.142 7.575 0.000 1.130 0.776
## bossy_Self 1.012 0.146 6.934 0.000 1.066 0.715
## contrllng_Slf 0.948 0.146 6.497 0.000 0.998 0.673
## grumpy_Self 1.080 0.150 7.216 0.000 1.137 0.742
## jealous_Self 0.806 0.139 5.818 0.000 0.849 0.607
## lazy_Self 0.817 0.151 5.393 0.000 0.861 0.565
## selfish_Self 0.950 0.138 6.884 0.000 1.001 0.710
## snobby_Self 1.097 0.142 7.696 0.000 1.155 0.787
## stubborn_Self 0.654 0.160 4.094 0.000 0.688 0.433
## calm =~
## calm_Self 1.000 0.748 0.651
## comfortng_Slf 1.071 0.215 4.985 0.000 0.801 0.574
## considert_Slf 1.056 0.163 6.486 0.000 0.790 0.786
## genuine_Self 1.098 0.177 6.206 0.000 0.821 0.743
## giving_Self 1.204 0.197 6.096 0.000 0.900 0.727
## helpful_Self 1.173 0.172 6.816 0.000 0.878 0.840
## humble_Self 0.893 0.187 4.778 0.000 0.668 0.547
## patient_Self 1.080 0.210 5.146 0.000 0.808 0.595
## studious_Self 0.642 0.191 3.352 0.001 0.480 0.372
## adventurous =~
## adventurs_Slf 1.000 1.233 0.826
## daring_Self 0.993 0.128 7.786 0.000 1.225 0.824
## risky_Self 0.671 0.121 5.554 0.000 0.828 0.583
## rulefllwr_Slf -0.171 0.118 -1.454 0.146 -0.211 -0.161
##
## Covariances:
## admired ~~
## agressive -0.087 0.131 -0.665 0.506 -0.073 -0.073
## calm 0.341 0.112 3.058 0.002 0.407 0.407
## adventurous 0.887 0.208 4.265 0.000 0.641 0.641
## agressive ~~
## calm -0.372 0.113 -3.305 0.001 -0.473 -0.473
## adventurous 0.319 0.161 1.979 0.048 0.246 0.246
## calm ~~
## adventurous 0.216 0.116 1.859 0.063 0.234 0.234
##
## Variances:
## admired_Self 0.952 0.146 0.952 0.431
## attractiv_Slf 0.836 0.127 0.836 0.457
## awkward_Self 1.534 0.230 1.534 0.544
## boring_Self 1.447 0.215 1.447 0.641
## confident_Slf 0.625 0.102 0.625 0.252
## cool_Self 0.977 0.149 0.977 0.433
## depressed_Slf 1.300 0.198 1.300 0.454
## flirty_Self 1.381 0.208 1.381 0.521
## insecure_Self 1.153 0.179 1.153 0.375
## leader_Self 1.349 0.202 1.349 0.564
## lonely_Self 1.290 0.196 1.290 0.463
## loner_Self 1.048 0.163 1.048 0.354
## outgoing_Self 1.461 0.221 1.461 0.474
## plain_Self 1.526 0.227 1.526 0.610
## poor_Self 1.726 0.254 1.726 0.730
## popular_Self 0.739 0.118 0.739 0.290
## pushover_Self 1.951 0.287 1.951 0.747
## shy_Self 1.800 0.268 1.800 0.614
## social_Self 0.766 0.122 0.766 0.294
## trendy_Self 0.825 0.129 0.825 0.344
## agressive_Slf 0.888 0.147 0.888 0.444
## angry_Self 0.844 0.144 0.844 0.398
## bossy_Self 1.086 0.176 1.086 0.489
## contrllng_Slf 1.203 0.190 1.203 0.547
## grumpy_Self 1.056 0.174 1.056 0.449
## jealous_Self 1.236 0.190 1.236 0.632
## lazy_Self 1.581 0.240 1.581 0.681
## selfish_Self 0.984 0.159 0.984 0.496
## snobby_Self 0.818 0.141 0.818 0.380
## stubborn_Self 2.049 0.304 2.049 0.812
## calm_Self 0.762 0.120 0.762 0.577
## comfortng_Slf 1.309 0.201 1.309 0.671
## considert_Slf 0.386 0.068 0.386 0.382
## genuine_Self 0.546 0.092 0.546 0.448
## giving_Self 0.723 0.120 0.723 0.472
## helpful_Self 0.322 0.063 0.322 0.295
## humble_Self 1.047 0.159 1.047 0.701
## patient_Self 1.193 0.184 1.193 0.646
## studious_Self 1.434 0.212 1.434 0.862
## adventurs_Slf 0.708 0.176 0.708 0.318
## daring_Self 0.707 0.174 0.707 0.320
## risky_Self 1.328 0.212 1.328 0.660
## rulefllwr_Slf 1.677 0.244 1.677 0.974
## admired 1.259 0.293 1.000 1.000
## agressive 1.110 0.269 1.000 1.000
## calm 0.559 0.164 1.000 1.000
## adventurous 1.521 0.338 1.000 1.000
Estimates of reliability vary below between the CFA and the alphas on the raw scales, but I’m not sure why.
## admired agressive calm adventurous total
## alpha 0.45964396 0.8920895 0.8575059 0.5014409 0.7726160
## omega 0.04277806 0.8937439 0.8602169 0.6814479 0.7210046
## omega2 0.04277806 0.8937439 0.8602169 0.6814479 0.7210046
## omega3 0.01204349 0.8920503 0.8605021 0.7219464 0.3250974
## avevar 0.52161736 0.4619776 0.4119190 0.4590871 0.4872755
##
## Reliability analysis
## Call: alpha(x = dataCFA[, itemScaleGroupsCFA$item[itemScaleGroupsCFA$maxPA ==
## "PA1"]], check.keys = T)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
## 0.95 0.95 0.97 0.51 20 0.014 3.7 1.2
##
## lower alpha upper 95% confidence boundaries
## 0.93 0.95 0.98
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## admired_Self 0.95 0.95 0.97 0.50 19 0.015
## attractive_Self 0.95 0.95 0.97 0.51 19 0.015
## awkward_Self- 0.95 0.95 0.97 0.51 20 0.015
## boring_Self- 0.95 0.95 0.97 0.51 20 0.015
## confident_Self 0.95 0.95 0.96 0.50 19 0.015
## cool_Self 0.95 0.95 0.97 0.50 19 0.015
## depressed_Self- 0.95 0.95 0.97 0.50 19 0.015
## flirty_Self 0.95 0.95 0.97 0.51 20 0.015
## insecure_Self- 0.95 0.95 0.97 0.50 19 0.015
## leader_Self 0.95 0.95 0.97 0.51 20 0.015
## lonely_Self- 0.95 0.95 0.97 0.50 19 0.015
## loner_Self- 0.95 0.95 0.97 0.50 19 0.015
## outgoing_Self 0.95 0.95 0.97 0.51 20 0.015
## plain_Self- 0.95 0.95 0.97 0.51 20 0.015
## poor_Self- 0.95 0.95 0.97 0.52 21 0.014
## popular_Self 0.95 0.95 0.97 0.50 19 0.015
## pushover_Self- 0.95 0.95 0.97 0.52 20 0.014
## shy_Self- 0.95 0.95 0.97 0.51 20 0.015
## social_Self 0.95 0.95 0.97 0.50 19 0.015
## trendy_Self 0.95 0.95 0.97 0.50 19 0.015
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## admired_Self 100 0.73 0.74 0.74 0.70 3.6 1.5
## attractive_Self 100 0.73 0.74 0.72 0.70 4.1 1.4
## awkward_Self- 100 0.73 0.72 0.71 0.69 3.4 1.7
## boring_Self- 100 0.66 0.65 0.64 0.61 4.2 1.5
## confident_Self 99 0.85 0.85 0.85 0.83 3.7 1.6
## cool_Self 99 0.74 0.74 0.74 0.71 3.8 1.5
## depressed_Self- 99 0.77 0.77 0.77 0.74 4.0 1.7
## flirty_Self 99 0.69 0.69 0.67 0.65 3.1 1.6
## insecure_Self- 100 0.82 0.82 0.81 0.80 3.5 1.8
## leader_Self 100 0.65 0.66 0.64 0.61 3.3 1.5
## lonely_Self- 100 0.77 0.77 0.76 0.74 3.8 1.7
## loner_Self- 100 0.82 0.82 0.81 0.79 3.9 1.7
## outgoing_Self 100 0.70 0.70 0.69 0.66 3.5 1.8
## plain_Self- 99 0.66 0.65 0.63 0.62 3.8 1.6
## poor_Self- 100 0.56 0.56 0.53 0.51 4.2 1.5
## popular_Self 99 0.83 0.83 0.83 0.80 3.3 1.6
## pushover_Self- 99 0.58 0.58 0.55 0.53 4.0 1.7
## shy_Self- 100 0.67 0.66 0.64 0.62 3.1 1.7
## social_Self 100 0.82 0.82 0.81 0.79 3.9 1.6
## trendy_Self 99 0.80 0.81 0.80 0.78 3.5 1.6
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## admired_Self 0.13 0.08 0.23 0.28 0.17 0.11 0.00
## attractive_Self 0.07 0.05 0.17 0.28 0.29 0.14 0.00
## awkward_Self 0.18 0.12 0.10 0.26 0.20 0.14 0.00
## boring_Self 0.27 0.23 0.15 0.21 0.09 0.05 0.00
## confident_Self 0.11 0.14 0.18 0.22 0.20 0.14 0.01
## cool_Self 0.11 0.09 0.18 0.28 0.20 0.13 0.01
## depressed_Self 0.26 0.18 0.18 0.15 0.12 0.10 0.01
## flirty_Self 0.21 0.21 0.14 0.19 0.16 0.08 0.01
## insecure_Self 0.19 0.15 0.15 0.17 0.17 0.17 0.00
## leader_Self 0.14 0.22 0.17 0.22 0.16 0.09 0.00
## lonely_Self 0.22 0.16 0.19 0.21 0.10 0.12 0.00
## loner_Self 0.25 0.18 0.14 0.18 0.13 0.12 0.00
## outgoing_Self 0.19 0.14 0.14 0.15 0.22 0.16 0.00
## plain_Self 0.18 0.17 0.22 0.18 0.14 0.10 0.01
## poor_Self 0.29 0.15 0.22 0.14 0.17 0.03 0.00
## popular_Self 0.17 0.16 0.21 0.23 0.10 0.12 0.01
## pushover_Self 0.27 0.18 0.10 0.21 0.17 0.06 0.01
## shy_Self 0.14 0.12 0.13 0.19 0.20 0.22 0.00
## social_Self 0.11 0.11 0.13 0.26 0.19 0.20 0.00
## trendy_Self 0.15 0.16 0.13 0.28 0.18 0.09 0.01
##
## Reliability analysis
## Call: alpha(x = dataCFA[, itemScaleGroupsCFA$item[itemScaleGroupsCFA$maxPA ==
## "PA2"]], check.keys = T)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
## 0.89 0.89 0.91 0.45 8.3 0.031 2.7 1.1
##
## lower alpha upper 95% confidence boundaries
## 0.83 0.89 0.95
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## agressive_Self 0.88 0.88 0.89 0.44 7.2 0.035
## angry_Self 0.87 0.87 0.88 0.43 6.9 0.036
## bossy_Self 0.88 0.88 0.89 0.45 7.2 0.035
## controlling_Self 0.88 0.88 0.89 0.45 7.3 0.035
## grumpy_Self 0.88 0.88 0.89 0.45 7.2 0.035
## jealous_Self 0.89 0.89 0.90 0.47 7.9 0.033
## lazy_Self 0.89 0.89 0.90 0.47 8.0 0.033
## selfish_Self 0.88 0.88 0.89 0.45 7.3 0.035
## snobby_Self 0.87 0.87 0.89 0.44 7.0 0.035
## stubborn_Self 0.90 0.90 0.91 0.49 8.6 0.032
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## agressive_Self 99 0.76 0.76 0.74 0.69 2.3 1.4
## angry_Self 100 0.81 0.81 0.81 0.75 2.5 1.5
## bossy_Self 100 0.75 0.75 0.73 0.67 2.6 1.5
## controlling_Self 100 0.74 0.74 0.71 0.66 2.6 1.5
## grumpy_Self 99 0.74 0.75 0.72 0.67 2.6 1.5
## jealous_Self 100 0.63 0.63 0.58 0.53 2.9 1.4
## lazy_Self 99 0.63 0.62 0.56 0.52 2.6 1.5
## selfish_Self 99 0.74 0.75 0.72 0.67 2.6 1.4
## snobby_Self 99 0.79 0.79 0.77 0.73 2.3 1.5
## stubborn_Self 100 0.54 0.53 0.45 0.42 3.5 1.6
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## agressive_Self 0.42 0.16 0.19 0.12 0.08 0.02 0.01
## angry_Self 0.34 0.24 0.17 0.15 0.05 0.05 0.00
## bossy_Self 0.32 0.22 0.16 0.17 0.09 0.04 0.00
## controlling_Self 0.29 0.29 0.12 0.17 0.09 0.04 0.00
## grumpy_Self 0.29 0.26 0.14 0.15 0.11 0.04 0.01
## jealous_Self 0.24 0.14 0.28 0.20 0.10 0.04 0.00
## lazy_Self 0.31 0.24 0.12 0.19 0.08 0.05 0.01
## selfish_Self 0.28 0.24 0.16 0.19 0.10 0.02 0.01
## snobby_Self 0.43 0.20 0.09 0.17 0.08 0.02 0.01
## stubborn_Self 0.15 0.13 0.22 0.20 0.18 0.12 0.00
##
## Reliability analysis
## Call: alpha(x = dataCFA[, itemScaleGroupsCFA$item[itemScaleGroupsCFA$maxPA ==
## "PA3"]], check.keys = T)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
## 0.86 0.87 0.88 0.42 6.6 0.037 4.5 0.84
##
## lower alpha upper 95% confidence boundaries
## 0.79 0.86 0.93
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## calm_Self 0.84 0.85 0.85 0.41 5.7 0.043
## comforting_Self 0.86 0.86 0.87 0.44 6.3 0.040
## considerate_Self 0.83 0.84 0.85 0.40 5.3 0.043
## genuine_Self 0.84 0.84 0.85 0.41 5.4 0.043
## giving_Self 0.84 0.85 0.86 0.42 5.7 0.042
## helpful_Self 0.83 0.84 0.84 0.40 5.3 0.043
## humble_Self 0.85 0.86 0.87 0.43 6.1 0.041
## patient_Self 0.85 0.86 0.86 0.43 6.1 0.041
## studious_Self 0.87 0.87 0.88 0.46 6.9 0.039
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## calm_Self 99 0.73 0.74 0.70 0.65 4.4 1.2
## comforting_Self 100 0.63 0.62 0.55 0.50 4.2 1.4
## considerate_Self 100 0.79 0.81 0.79 0.73 4.8 1.0
## genuine_Self 100 0.77 0.78 0.75 0.69 4.7 1.1
## giving_Self 100 0.72 0.72 0.68 0.62 4.6 1.3
## helpful_Self 100 0.80 0.81 0.80 0.74 4.8 1.1
## humble_Self 100 0.65 0.65 0.58 0.53 4.4 1.2
## patient_Self 99 0.67 0.66 0.61 0.55 4.1 1.3
## studious_Self 100 0.52 0.51 0.41 0.37 4.4 1.3
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## calm_Self 0.01 0.07 0.10 0.28 0.35 0.18 0.01
## comforting_Self 0.06 0.09 0.08 0.35 0.24 0.18 0.00
## considerate_Self 0.00 0.02 0.09 0.25 0.34 0.30 0.00
## genuine_Self 0.00 0.04 0.08 0.29 0.29 0.30 0.00
## giving_Self 0.01 0.10 0.03 0.31 0.28 0.27 0.00
## helpful_Self 0.00 0.04 0.06 0.27 0.34 0.29 0.00
## humble_Self 0.04 0.02 0.15 0.31 0.29 0.19 0.00
## patient_Self 0.03 0.12 0.13 0.27 0.28 0.16 0.01
## studious_Self 0.02 0.07 0.13 0.31 0.24 0.23 0.00
##
## Reliability analysis
## Call: alpha(x = dataCFA[, itemScaleGroupsCFA$item[itemScaleGroupsCFA$maxPA ==
## "PA4"]], check.keys = T)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
## 0.72 0.71 0.73 0.38 2.4 0.082 3.2 1.1
##
## lower alpha upper 95% confidence boundaries
## 0.55 0.72 0.88
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## adventurous_Self 0.66 0.66 0.58 0.39 1.9 0.108
## daring_Self 0.50 0.50 0.47 0.25 1.0 0.126
## risky_Self 0.60 0.59 0.64 0.33 1.5 0.112
## rulefollower_Self- 0.79 0.78 0.73 0.55 3.6 0.091
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## adventurous_Self 100 0.73 0.72 0.65 0.49 4.0 1.5
## daring_Self 100 0.87 0.86 0.85 0.73 3.2 1.5
## risky_Self 100 0.79 0.78 0.66 0.58 2.9 1.4
## rulefollower_Self- 100 0.54 0.56 0.34 0.25 2.7 1.4
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## adventurous_Self 0.07 0.14 0.12 0.23 0.31 0.13 0
## daring_Self 0.17 0.16 0.16 0.34 0.10 0.07 0
## risky_Self 0.21 0.22 0.23 0.18 0.12 0.04 0
## rulefollower_Self 0.04 0.08 0.11 0.29 0.27 0.21 0
What conclusions can we draw? The CFA indicates that we could do better in this model. But the scale alphas coefficients are very good, with even the 4 item adventurous factor getting >.7. However, there are a lot of cross loadings in the EFA, and we totally ignore those, which is why the CFA fit is so shabby. This can especially be the case with many items per scale.